Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. #26029120 | C2 | semidirect |
| 5. #26018349 | C2 | semidirect |
| 6. #26018342 | C2 | semidirect |
| 7. C2×#362×C89 | C2 | semidirect |
| 12. C2×#15667955 | C4 | semidirect |
| 162. C2×#362 | D89 | semidirect |
| 167. C89 | #13018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667955 | 2 |
| #26029120 | 2 |
| #26021969 | 2 |
| #26021160 | 2 |
| #26018349 | 2 |
| #26018342 | 2 |
| C2×#362×C89 | 2 |
| #13018 | 89 |