Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1140 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 175 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. #26028534 | C2 | semidirect |
| 2. #26021678 | C2 | semidirect |
| 3. #26021434 | C2 | semidirect |
| 4. #26021431 | C2 | semidirect |
| 5. #26021248 | C2 | semidirect |
| 6. #26020162 | C2 | semidirect |
| 7. C89×#2847 | C2 | semidirect |
| 8. C22×#13083559 | C22 | semidirect |
| 11. C2×#15667945 | C22 | semidirect |
| 12. C2×#15667933 | C22 | semidirect |
| 13. C2×#15667932 | C22 | semidirect |
| 18. #19151360 | C22 | semidirect |
| 19. #19151360 | C22 | semidirect |
| 75. C24×C89 | D8 | semidirect |
| 171. #2847 | D89 | semidirect |
| 177. C89 | #32706 | semidirect |
| 230. C24 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028534 | 2 |
| #26021678 | 2 |
| #26021434 | 2 |
| #26021431 | 2 |
| #26021248 | 2 |
| #26020162 | 2 |
| C89×#2847 | 2 |
| #32706 | 89 |