Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
378 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #26030791 | C2 | semidirect |
| 5. #26018361 | C2 | semidirect |
| 6. #26018348 | C2 | semidirect |
| 7. C89×#1379 | C2 | semidirect |
| 31. C2×D712 | Q8 | semidirect |
| 165. #1379 | D89 | semidirect |
| 166. C89 | #13369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030791 | 2 |
| #26021969 | 2 |
| C2×#19151400 | 2 |
| #26021162 | 2 |
| #26018361 | 2 |
| #26018348 | 2 |
| C89×#1379 | 2 |
| #13369 | 89 |