Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26033390 | C2 | semidirect |
| 2. C2×#19151433 | C2 | semidirect |
| 3. #26022369 | C2 | semidirect |
| 4. #26018443 | C2 | semidirect |
| 5. #26018436 | C2 | semidirect |
| 6. #26018395 | C2 | semidirect |
| 7. C89×#2263 | C2 | semidirect |
| 17. C2×#15667918 | C22 | semidirect |
| 18. #19151428 | C22 | semidirect |
| 21. C2×D16×C89 | C22 | semidirect |
| 24. M64×C89 | C22 | semidirect |
| 123. #2263 | D89 | semidirect |
| 129. C89 | #13669 | semidirect |
| 137. C2×D16 | C2×D89 | semidirect |
| 143. M64 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033390 | 2 |
| C2×#19151433 | 2 |
| #26022369 | 2 |
| #26018443 | 2 |
| #26018436 | 2 |
| #26018395 | 2 |
| C89×#2263 | 2 |
| #13669 | 89 |