Subgroups — C₂×#11761612 #14524048

Order 2144.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11761612	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₆₇⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₆₇	C₄	1	1	yes	characteristic
5	C₂×C₄×C₆₇	C₄	1	2	yes	—
6	C₂×C₄×C₆₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₆₇	C₂²	1	2	yes	—
8	C₂×C₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₆₇⋊C₈	C₂²	1	4	yes	complemented
10	C₂²×C₆₇	—	2	2	no	—
11	C₂²×C₆₇	C₂×C₄	1	2	yes	—
12	C₂²×C₆₇	C₂×C₄	1	1	yes	characteristic
13	C₄×C₆₇	C₂×C₄	1	2	yes	—
14	C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
15	C₄×C₆₇	C₂³	1	1	yes	characteristic
16	C₂×C₆₇	—	2	2	no	—
17	C₂×C₆₇	M₁₆	1	2	yes	complemented
18	C₂×C₆₇	C₂²×C₄	1	1	yes	characteristic
19	C₆₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₂×M₁₆	—	67	1	no	maximal, Sylow
21	C₂²×C₄	D₆₇	1	1	yes	characteristic
22	M₁₆	—	67	4	no	—
23	C₂×C₈	—	67	2	no	—
24	C₂³	Dic₆₇	1	1	yes	characteristic
25	C₂×C₄	Dic₆₇	1	1	yes	characteristic
26	C₂×C₄	Dic₆₇	1	2	yes	—
27	C₂×C₄	C₂×D₆₇	1	2	yes	—
28	C₂×C₄	C₂×D₆₇	1	1	yes	characteristic
29	C₈	—	67	4	no	—
30	C₂²	—	2	2	no	—
31	C₂²	C₂×Dic₆₇	1	2	yes	—
32	C₂²	C₂×Dic₆₇	1	1	yes	characteristic
33	C₄	C₂×Dic₆₇	1	2	yes	—
34	C₄	C₂×Dic₆₇	1	1	yes	characteristic
35	C₄	C₂²×D₆₇	1	1	yes	characteristic
36	C₂	—	2	2	no	—
37	C₂	#11761612	1	2	yes	direct product factor
38	C₂	C₂²×Dic₆₇	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.