Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26033354 | C2 | semidirect |
| 3. C2×#19151411 | C2 | semidirect |
| 4. #26020299 | C2 | semidirect |
| 5. #26018367 | C2 | semidirect |
| 6. #26018366 | C2 | semidirect |
| 7. C2×#361×C89 | C2 | semidirect |
| 41. #15667952 | D4 | semidirect |
| 62. M32×C89 | D4 | semidirect |
| 172. C2×#361 | D89 | semidirect |
| 176. C89 | #13079 | semidirect |
| 222. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26029896 | 2 |
| C2×#19151411 | 2 |
| #26020299 | 2 |
| #26018367 | 2 |
| #26018366 | 2 |
| C2×#361×C89 | 2 |
| #13079 | 89 |