Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26023010 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#1511 | C2 | semidirect |
| 11. #19151753 | C4 | semidirect |
| 12. #19151748 | C4 | semidirect |
| 271. #1511 | D89 | semidirect |
| 274. C89 | #9524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029510 | 2 |
| #26023010 | 2 |
| #26020195 | 2 |
| #26020169 | 2 |
| #26018161 | 2 |
| #26018104 | 2 |
| C89×#1511 | 2 |
| #9524 | 89 |