Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
280 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #19153211 |
| commutator, cosocle, hypocenter | C72×C13 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C13 | C32 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C22 | |
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.
| subgroup | index |
|---|---|
| C2×#19153211 | 2 |
| C22×#14274262 | 3 |
| C22×C7×#63270 | 3 |
| C22×C13×#3862 | 3 |
| C22×ΓL(1,𝔽8)×C13⋊C3 | 7 |
| C22×ΓL(1,𝔽8)2 | 13 |