Subgroups — C₂²×#20238494 #37558503

Order 23824.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20238494	C₂	1	6	yes	maximal, direct product factor
2	C₂²×D₁₄₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₄₈₉	C₄	1	1	yes	characteristic, complemented
4	C₂×D₁₄₈₉	C₄	1	3	yes	complemented
5	C₂×D₁₄₈₉	C₂²	1	3	yes	—
6	#20238494	C₂²	1	4	yes	direct product factor
7	C₂×C₁₄₈₉	C₂×C₄	1	3	yes	complemented
8	D₁₄₈₉	C₂×C₄	1	3	yes	complemented
9	D₁₄₈₉	C₂³	1	1	yes	characteristic
10	C₁₄₈₉	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₂²×C₄	—	1489	1	no	maximal, Sylow
12	C₂³	—	1489	1	no	—
13	C₂×C₄	—	1489	6	no	—
14	C₂²	—	1489	3	no	—
15	C₂²	—	1489	3	no	—
16	C₂²	#20238494	1	1	yes	characteristic, direct product factor
17	C₄	—	1489	4	no	—
18	C₂	—	1489	1	no	—
19	C₂	—	1489	3	no	—
20	C₂	C₂×#20238494	1	3	yes	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.