Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
378 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 378 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 |
|---|---|---|
| 2. #26021599 | C2 | semidirect |
| 4. #26018282 | C2 | semidirect |
| 6. #26018195 | C2 | semidirect |
| 7. C89×#1605 | C2 | semidirect |
| 180. #1605 | D89 | semidirect |
| 185. C89 | #12239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027960 | 2 |
| #26021599 | 2 |
| #26019192 | 2 |
| #26018282 | 2 |
| #26018256 | 2 |
| #26018195 | 2 |
| C89×#1605 | 2 |
| #12239 | 89 |