Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26022065 | C2 | semidirect |
| 3. #26020008 | C2 | semidirect |
| 5. #26018240 | C2 | semidirect |
| 7. C89×#1342 | C2 | semidirect |
| 9. #19151995 | C4 | semidirect |
| 10. #19151983 | C4 | semidirect |
| 14. #19151709 | C4 | semidirect |
| 15. #19151705 | C4 | semidirect |
| 148. #1342 | D89 | semidirect |
| 152. C89 | #11769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030870 | 2 |
| #26022065 | 2 |
| #26020008 | 2 |
| #26018242 | 2 |
| #26018240 | 2 |
| #26018238 | 2 |
| C89×#1342 | 2 |
| #11769 | 89 |