Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
312 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26021042 | C2 | semidirect |
| 5. #26018367 | C2 | semidirect |
| 6. #26018348 | C2 | semidirect |
| 7. C89×#2108 | C2 | semidirect |
| 15. #19151415 | C4 | semidirect |
| 16. #19151412 | C4 | semidirect |
| 143. #2108 | D89 | semidirect |
| 148. C89 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022002 | 2 |
| C2×#19151406 | 2 |
| #26021150 | 2 |
| #26021042 | 2 |
| #26018367 | 2 |
| #26018348 | 2 |
| C89×#2108 | 2 |
| #13146 | 89 |