Subgroups — #14524039

Order 2144.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊D₆₇	C₂	1	4	yes	maximal, complemented
3	C₄×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₆₇	C₂²	1	2	yes	—
6	C₂²×D₆₇	C₂²	1	2	yes	—
7	D₄×C₆₇	—	2	2	no	—
8	C₂×C₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₂²⋊D₆₇	—	2	8	no	—
10	C₂×Dic₆₇	C₂²	1	2	yes	—
11	D₂₆₈	—	2	2	no	—
12	C₂²×C₆₇	—	2	4	no	—
13	C₂²×C₆₇	—	2	2	no	—
14	C₂²×C₆₇	C₂³	1	1	yes	characteristic
15	C₂×D₆₇	—	2	2	no	—
16	C₂×D₆₇	—	2	4	no	—
17	C₄×C₆₇	D₄	1	2	yes	complemented
18	Dic₆₇	D₄	1	4	yes	complemented
19	C₂×C₆₇	—	4	2	no	—
20	C₂×C₆₇	C₂×D₄	1	2	yes	—
21	C₂×C₆₇	C₂×D₄	1	1	yes	characteristic
22	D₆₇	—	4	2	no	—
23	C₆₇	#127	1	1	yes	characteristic, complemented, Sylow
24	#127	—	67	1	no	maximal, Sylow
25	C₂×D₄	—	67	4	no	—
26	C₂×D₄	—	67	1	no	—
27	C₂×D₄	D₆₇	1	1	yes	characteristic, complemented
28	C₄²	—	67	1	no	—
29	C₂³	—	67	2	no	—
30	C₂³	C₂×D₆₇	1	2	yes	—
31	D₄	—	2	2	no	—
32	D₄	—	134	8	no	—
33	D₄	—	134	2	no	—
34	C₂×C₄	—	67	2	no	—
35	C₂×C₄	C₂×D₆₇	1	1	yes	characteristic
36	C₂²	—	2	4	no	—
37	C₂²	—	2	2	no	—
38	C₂²	—	134	4	no	—
39	C₂²	—	134	2	no	—
40	C₂²	C₂²×D₆₇	1	1	yes	characteristic
41	C₄	—	67	4	no	—
42	C₄	C₂²⋊D₆₇	1	2	yes	complemented
43	C₂	—	4	2	no	—
44	C₂	—	268	2	no	—
45	C₂	D₄×D₆₇	1	2	yes	—
46	C₂	C₂×C₂²⋊D₆₇	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.