Subgroups — C₄⋊(D₃₇⋊C₃) #11725152

Order 888.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₇⋊C₃	C₂	1	2	yes	maximal, complemented
2	C₄×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₄₈	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₃₇⋊C₃	C₂²	1	1	yes	characteristic
5	D₃₇⋊C₃	—	2	2	no	—
6	C₂×D₃₇	C₂×C₃	1	2	yes	complemented
7	C₄×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃₇⋊C₃	D₄	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃₇	C₂²×C₃	1	1	yes	characteristic
10	D₃₇	—	2	2	no	—
11	C₃₇	C₃×D₄	1	1	yes	characteristic, complemented, Sylow
12	C₃×D₄	—	37	1	no	maximal, Hall
13	C₂²×C₃	—	37	2	no	—
14	C₃×C₄	—	37	1	no	—
15	D₄	—	37	1	no	Sylow
16	C₂×C₃	—	37	1	no	—
17	C₂×C₃	—	74	2	no	—
18	C₂²	—	37	2	no	—
19	C₄	D₃₇⋊C₃	1	1	yes	characteristic, complemented
20	C₃	—	37	1	no	Sylow
21	C₂	—	74	2	no	—
22	C₂	C₂×D₃₇⋊C₃	1	1	yes	characteristic

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.