Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26023432 | C2 | semidirect |
| 3. #26018977 | C2 | semidirect |
| 6. #26018117 | C2 | semidirect |
| 7. C89×#1288 | C2 | semidirect |
| 12. #19151978 | C4 | semidirect |
| 13. #19151971 | C4 | semidirect |
| 163. #1288 | D89 | semidirect |
| 164. C89 | #9429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030711 | 2 |
| #26023432 | 2 |
| #26018977 | 2 |
| #26018800 | 2 |
| #26018798 | 2 |
| #26018117 | 2 |
| C89×#1288 | 2 |
| #9429 | 89 |