# gps_subgroup_search downloaded from the LMFDB on 25 July 2026.
# Search link: https://www.lmfdb.org/Groups/Abstract/Subgroups?subgroup=104976.cf
# Query "{'subgroup': '104976.cf'}" returned 20 gps_subgroup_searchs, sorted by ambient order.

# Each entry in the following data list has the form:
#    [Label, Subgroup, Ambient, Quotient]
# For more details, see the definitions at the bottom of the file.



"104976.cf.1.a1"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, true, true, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976]	[["1.1", "C_1"], 1, false, true, true, true, true, true, false, true, true]
"209952.dj.2.B"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, true, true, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["209952.dj", "C_3^6:(S_3\\times \\GL(2,3))"], 209952]	[["2.1", "C_2"], 2, false, true, true, true, true, true, true, true, true]
"419904.fx.4.B"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["419904.fx", "C_3^6:(A_4\\times \\GL(2,3))"], 419904]	[[NULL, NULL], 4, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"839808.hi.8.I"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["839808.hi", "C_3^6.(S_4\\times \\GL(2,3))"], 839808]	[[NULL, NULL], 8, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"944784.ko.9.B"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, true, false, false, false, false, false, true, false, false, false, false, false, false]	[["944784.ko", "C_3^8.(C_3\\times \\GL(2,3))"], 944784]	[[NULL, NULL], 9, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"1889568.mo.18.H"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["1889568.mo", "C_3^8.(S_3\\times \\GL(2,3))"], 1889568]	[[NULL, NULL], 18, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"3779136.ph.36.F"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["3779136.ph", "C_3^8.\\GL(2,3):A_4"], 3779136]	[[NULL, NULL], 36, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"3779136.pi.36.O"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["3779136.pi", "C_3^8.(A_4\\times \\GL(2,3))"], 3779136]	[[NULL, NULL], 36, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"3779136.pi.36.P"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["3779136.pi", "C_3^8.(A_4\\times \\GL(2,3))"], 3779136]	[[NULL, NULL], 36, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"6718464.ey.64.B"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["6718464.ey", "C_3^6.Q_8\\wr C_3:S_3"], 6718464]	[[NULL, NULL], 64, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"7558272.om.72.DV"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["7558272.om", "C_3^8.(S_4\\times \\GL(2,3))"], 7558272]	[[NULL, NULL], 72, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"7558272.om.72.DW"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["7558272.om", "C_3^8.(S_4\\times \\GL(2,3))"], 7558272]	[[NULL, NULL], 72, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"7558272.on.72.X"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["7558272.on", "C_3^8.\\GL(2,3):S_4"], 7558272]	[[NULL, NULL], 72, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"7558272.on.72.Y"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["7558272.on", "C_3^8.\\GL(2,3):S_4"], 7558272]	[[NULL, NULL], 72, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"8503056.fr.81._.C"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["8503056.fr", "C_3^8.C_3^3:\\GL(2,3)"], 8503056]	[[NULL, NULL], 81, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"13436928.dt.128.I"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["13436928.dt", "C_3^6.Q_8\\wr S_3:S_3"], 13436928]	[[NULL, NULL], 128, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"15116544.lw.144.ET"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["15116544.lw", "C_3^6.(C_3^2:\\GL(2,3)\\times \\GL(2,3))"], 15116544]	[[NULL, NULL], 144, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"17006112.fx.162._.I"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["17006112.fx", "C_3^{10}.Q_8.S_3^2"], 17006112]	[[NULL, NULL], 162, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"20155392.bd.192.H"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["20155392.bd", "C_3^6.Q_8\\wr C_3:C_3:S_3"], 20155392]	[[NULL, NULL], 192, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]
"40310784.v.384.BH"	[["104976.cf", "C_3^6:(C_3\\times \\GL(2,3))"], 104976, 0, false, false, false, false, false, false, false, false, true, false, false, false, false, false, false]	[["40310784.v", "C_3^6.Q_8\\wr C_3:S_3:S_3"], 40310784]	[[NULL, NULL], 384, false, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL]


# Label --
#    The full label of a subgroup is of the form $\mathtt{N.i.m.a}$ or $\mathtt{N.i.m.a.j}$.  In either case, $\mathtt{N.i}$ is the label of the ambient group, $\mathtt{m}$ is the index of the subgroup in the ambient group, $\mathtt{a}$ distinguishes subgroups up to automorphism and $\mathtt{j}$ distinguishes subgroups up to conjugacy.  Both $\mathtt{a}$ and $\mathtt{j}$ take the form of a sequence of letters followed by an ordinal. The letters are a base 26 (a=0, z=25) encoding of the ordering up to Gassmann-equivalence, and the integer following distinguishes groups in the same Gassmann class.  (For details on how we label Gassmann classes and order subgroups within a Gassmann class, see Computing labels of subgroups.) For some ambient groups, we only compute subgroups up to automorphism (in which case the first form is used, omitting the $\mathtt{j}$.

#    When the ambient group is clear from context, sometimes the short label $\mathtt{m.a}$ or $\mathtt{m.a.j}$ is used instead.