Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26018138 | C2 | semidirect |
| 5. #26018137 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#1284 | C2 | semidirect |
| 14. #19151465 | C4 | semidirect |
| 15. #19151457 | C4 | semidirect |
| 19. #19151443 | C4 | semidirect |
| 20. #95×D89 | C4 | semidirect |
| 219. #1284 | D89 | semidirect |
| 220. C89 | #8776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023189 | 2 |
| C4×#15667926 | 2 |
| #26018588 | 2 |
| #26018138 | 2 |
| #26018137 | 2 |
| #26018104 | 2 |
| C89×#1284 | 2 |
| #8776 | 89 |