Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #26021971 | C2 | semidirect |
| 5. #26021165 | C2 | semidirect |
| 6. #26018340 | C2 | semidirect |
| 7. C89×#1382 | C2 | semidirect |
| 13. C2×#15667957 | C4 | semidirect |
| 33. C2×Dic356 | C2×C4 | semidirect |
| 59. C2×C16×C89 | C2×C4 | semidirect |
| 166. #1382 | D89 | semidirect |
| 168. C89 | #13019 | semidirect |
| 215. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667957 | 2 |
| #26029103 | 2 |
| C2×#19151410 | 2 |
| #26021971 | 2 |
| #26021165 | 2 |
| #26018340 | 2 |
| C89×#1382 | 2 |
| #13019 | 89 |