Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26022180 | C2 | semidirect |
| 3. #26021563 | C2 | semidirect |
| 4. #26018264 | C2 | semidirect |
| 5. #26018261 | C2 | semidirect |
| 6. #26018192 | C2 | semidirect |
| 7. C89×#3250 | C2 | semidirect |
| 181. #3250 | D89 | semidirect |
| 188. C89 | #12160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022180 | 2 |
| #26022163 | 2 |
| #26021563 | 2 |
| #26018264 | 2 |
| #26018261 | 2 |
| #26018192 | 2 |
| C89×#3250 | 2 |
| #12160 | 89 |