Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26023546 | C2 | semidirect |
| 4. #26018155 | C2 | semidirect |
| 5. #26018154 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 54. C4⋊Q8×C89 | Q8 | semidirect |
| 55. #127×C89 | Q8 | semidirect |
| 203. C89 | #10370 | semidirect |
| 226. C4⋊Q8 | Dic178 | semidirect |
| 227. #127 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023546 | 2 |
| #26021085 | 2 |
| #26018747 | 2 |
| #26018155 | 2 |
| #26018154 | 2 |
| #26018080 | 2 |
| C89×#1502 | 2 |
| #10370 | 89 |