Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C2×#15667958 | C4 | semidirect |
| 162. C89 | #13020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667958 | 2 |
| #26029120 | 2 |
| #26021973 | 2 |
| #26021165 | 2 |
| #26018349 | 2 |
| #26018342 | 2 |
| C2×#362×C89 | 2 |
| #13020 | 89 |