Subgroups — C₂×#27134395 #37589999

Order 24608.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27134395	C₂	1	2	yes	maximal, direct product factor
2	C₂×#20259679	C₂	1	1	yes	maximal, characteristic
3	#20259679	C₄	1	1	yes	characteristic
4	#20259679	C₂²	1	1	yes	characteristic
5	C₂×#15690484	C₄	1	1	yes	characteristic
6	C₂×D₇₆₉	C₈	1	1	yes	characteristic
7	#15690484	C₈	1	1	yes	characteristic
8	#15690484	C₂×C₄	1	1	yes	characteristic
9	C₂×C₇₆₉	C₁₆	1	1	yes	characteristic, complemented
10	D₇₆₉	C₁₆	1	1	yes	characteristic, complemented
11	D₇₆₉	C₂×C₈	1	1	yes	characteristic
12	C₇₆₉	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₆	—	769	1	no	maximal, Sylow
14	C₂×C₈	—	769	1	no	—
15	C₁₆	—	769	2	no	—
16	C₂×C₄	—	769	1	no	—
17	C₈	—	769	1	no	—
18	C₈	—	769	1	no	—
19	C₂²	—	769	1	no	—
20	C₄	—	769	1	no	—
21	C₄	—	769	1	no	—
22	C₂	—	769	1	no	—
23	C₂	—	769	1	no	—
24	C₂	#27134395	1	1	yes	characteristic, direct product factor

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.