Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26022017 | C2 | semidirect |
| 5. #26020375 | C2 | semidirect |
| 6. #26018350 | C2 | semidirect |
| 7. C89×#1386 | C2 | semidirect |
| 11. #19151709 | C4 | semidirect |
| 12. #19151704 | C4 | semidirect |
| 156. #1386 | 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 |
|---|---|
| #26029135 | 2 |
| #26022017 | 2 |
| #26021987 | 2 |
| #26021981 | 2 |
| #26020375 | 2 |
| #26018350 | 2 |
| C89×#1386 | 2 |
| #12828 | 89 |