Subgroups — #14524040

Order 2144.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₆₈	C₂	1	6	yes	maximal, complemented
2	C₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₆₇	C₂²	1	4	yes	—
4	C₂×C₄×C₆₇	C₂²	1	3	yes	—
5	D₂₆₈	—	2	12	no	—
6	C₂²×C₆₇	C₂³	1	1	yes	characteristic
7	C₂×D₆₇	—	2	12	no	—
8	C₄×C₆₇	D₄	1	6	yes	complemented
9	C₂×C₆₇	C₂×D₄	1	3	yes	—
10	D₆₇	—	4	4	no	—
11	C₆₇	#127	1	1	yes	characteristic, complemented, Sylow
12	#127	—	67	1	no	maximal, Sylow
13	C₂×D₄	—	67	6	no	—
14	C₄²	D₆₇	1	1	yes	characteristic, complemented
15	C₂³	—	67	4	no	—
16	D₄	—	134	12	no	—
17	C₂×C₄	C₂×D₆₇	1	3	yes	—
18	C₂²	—	134	12	no	—
19	C₂²	C₂²×D₆₇	1	1	yes	characteristic
20	C₄	D₂₆₈	1	6	yes	complemented
21	C₂	—	268	4	no	—
22	C₂	C₂×D₂₆₈	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.