Subgroups — C₃×#22582995 #41008772

Order 26988.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×D₁₇₃	C₂	1	1	yes	maximal, characteristic
2	#22582995	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₃×C₁₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₁₇₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₇₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#10621924	—	13	1	no	maximal, Hall
7	C₃×D₁₇₃	D₁₃	1	1	yes	characteristic
8	#10621924	—	13	1	no	Hall
9	C₃×C₁₇₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
10	D₁₇₃	C₃×D₁₃	1	1	yes	characteristic
11	C₁₇₃	C₃×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
12	C₃×Dic₁₃	—	173	1	no	maximal, Hall
13	C₂×C₃×C₁₃	—	173	1	no	—
14	Dic₁₃	—	173	1	no	Hall
15	C₃×C₁₃	#10621924	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	—	173	1	no	—
17	C₁₃	C₃×#10621924	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2249	1	no	Hall
19	C₂×C₃	—	173	1	no	—
20	C₄	—	2249	1	no	Sylow
21	C₃	#22582995	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	173	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.