Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26020376 | C2 | semidirect |
| 5. #26018358 | C2 | semidirect |
| 6. #26018351 | C2 | semidirect |
| 7. C89×#2153 | C2 | semidirect |
| 10. #19151711 | C4 | semidirect |
| 11. #19151706 | C4 | semidirect |
| 152. #2153 | D89 | semidirect |
| 158. C89 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029137 | 2 |
| #26021989 | 2 |
| #26021981 | 2 |
| #26020376 | 2 |
| #26018358 | 2 |
| #26018351 | 2 |
| C89×#2153 | 2 |
| #12828 | 89 |