Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26022026 | C2 | semidirect |
| 5. #26018353 | C2 | semidirect |
| 6. #26018334 | C2 | semidirect |
| 7. C89×#1945 | C2 | semidirect |
| 20. #19151407 | C4 | semidirect |
| 43. #15667952 | C2×C4 | semidirect |
| 58. #106×C89 | C2×C4 | semidirect |
| 159. #1945 | D89 | semidirect |
| 162. C89 | #12951 | semidirect |
| 211. #106 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668034 | 2 |
| #26022026 | 2 |
| #26021999 | 2 |
| #26021987 | 2 |
| #26018353 | 2 |
| #26018334 | 2 |
| C89×#1945 | 2 |
| #12951 | 89 |