Subgroups — #17994211

Order 4736.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557910	C₂	1	6	yes	maximal, complemented
2	C₈²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₉₆	—	2	12	no	—
4	#11924533	C₂²	1	4	yes	—
5	C₄×C₈×C₃₇	C₂²	1	3	yes	—
6	C₂×D₁₄₈	—	2	12	no	—
7	C₂×C₈×C₃₇	D₄	1	6	yes	—
8	C₄²×C₃₇	C₂³	1	1	yes	characteristic
9	D₂₉₆	—	4	24	no	—
10	C₂²×D₃₇	—	4	4	no	—
11	C₂×C₄×C₃₇	C₂×D₄	1	3	yes	—
12	D₁₄₈	—	4	24	no	—
13	C₈×C₃₇	D₈	1	12	yes	complemented
14	C₂²×C₃₇	#127	1	1	yes	characteristic
15	C₂×D₃₇	—	8	12	no	—
16	C₄×C₃₇	C₂×D₈	1	6	yes	—
17	#1712	—	37	1	no	maximal, Sylow
18	C₂×C₃₇	#493	1	3	yes	—
19	D₃₇	—	16	4	no	—
20	#493	—	37	6	no	—
21	C₈²	D₃₇	1	1	yes	characteristic, complemented
22	C₃₇	#1712	1	1	yes	characteristic, complemented, Sylow
23	C₂×D₈	—	74	12	no	—
24	#127	—	37	4	no	—
25	C₄×C₈	C₂×D₃₇	1	3	yes	—
26	C₂×D₄	—	74	12	no	—
27	D₈	—	148	24	no	—
28	C₂×C₈	D₁₄₈	1	6	yes	—
29	C₄²	C₂²×D₃₇	1	1	yes	characteristic
30	C₂³	—	148	4	no	—
31	D₄	—	148	24	no	—
32	C₂×C₄	C₂×D₁₄₈	1	3	yes	—
33	C₈	D₂₉₆	1	12	yes	complemented
34	C₂²	—	296	12	no	—
35	C₂²	#11924533	1	1	yes	characteristic
36	C₄	C₂×D₂₉₆	1	6	yes	—
37	C₂	—	592	4	no	—
38	C₂	#14557910	1	3	yes	—

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.