Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
344 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26021942 | C2 | semidirect |
| 3. #26021920 | C2 | semidirect |
| 4. #26018427 | C2 | semidirect |
| 5. #26018410 | C2 | semidirect |
| 6. #26018408 | C2 | semidirect |
| 7. C89×#1414 | C2 | semidirect |
| 8. #19152204 | C4 | semidirect |
| 11. #19151975 | C4 | semidirect |
| 12. #19151964 | C4 | semidirect |
| 17. #19151657 | C4 | semidirect |
| 35. #15668009 | C2×C4 | semidirect |
| 54. #15667923 | C2×C4 | semidirect |
| 55. #125×C89 | C2×C4 | semidirect |
| 61. C4×C8×C89 | C2×C4 | semidirect |
| 174. #1414 | D89 | semidirect |
| 177. C89 | #13605 | semidirect |
| 207. #125 | C4×D89 | semidirect |
| 231. C4×C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031305 | 2 |
| #26021942 | 2 |
| #26021920 | 2 |
| #26018427 | 2 |
| #26018410 | 2 |
| #26018408 | 2 |
| C89×#1414 | 2 |
| #13605 | 89 |