Subgroups — #14558440

Order 2368.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924595	C₂	1	2	yes	maximal
2	#11924524	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
4	C₂×Dic₇₄	C₄	1	1	yes	characteristic, complemented
5	C₂²⋊#3866	—	2	2	no	—
6	C₄²×C₃₇	C₄	1	1	yes	characteristic, complemented
7	#10596938	—	2	2	no	—
8	C₂²×D₃₇	D₄	1	2	yes	—
9	C₂×#3866	—	4	2	no	—
10	C₂×C₄×C₃₇	—	2	1	no	—
11	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₃₇	—	2	1	no	—
13	D₁₄₈	—	4	1	no	—
14	Dic₇₄	—	4	1	no	—
15	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₃₇	—	2	2	no	—
17	C₂×D₃₇	—	4	2	no	—
18	#3866	—	8	2	no	—
19	C₄×C₃₇	—	2	1	no	—
20	C₄×C₃₇	—	4	1	no	—
21	Dic₃₇	—	4	1	no	—
22	C₂×C₃₇	—	2	1	no	—
23	C₂×C₃₇	#99	1	1	yes	characteristic
24	D₃₇	—	4	2	no	—
25	#354	—	37	1	no	maximal, Sylow
26	C₃₇	#354	1	1	yes	characteristic, complemented, Sylow
27	#124	—	37	1	no	—
28	#99	—	37	2	no	—
29	C₂×Q₈	—	37	1	no	—
30	C₂×D₄	—	37	1	no	—
31	C₂²⋊C₄	—	74	2	no	—
32	C₂²⋊C₄	—	74	2	no	—
33	C₄²	#3866	1	1	yes	characteristic, complemented
34	C₂³	—	37	2	no	—
35	Q₈	—	148	1	no	—
36	D₄	—	148	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	74	1	no	—
39	C₂×C₄	—	148	2	no	—
40	C₂×C₄	C₂×#3866	1	1	yes	characteristic
41	C₂²	—	74	2	no	—
42	C₂²	—	148	2	no	—
43	C₂²	C₂²⋊#3866	1	1	yes	characteristic
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	296	2	no	—
47	C₄	—	148	1	no	—
48	C₂	—	2	1	no	—
49	C₂	—	148	2	no	—
50	C₂	#11924595	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.