Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26020239 | C2 | semidirect |
| 3. #26018587 | C2 | semidirect |
| 4. #26018274 | C2 | semidirect |
| 5. #26018272 | C2 | semidirect |
| 6. #26018249 | C2 | semidirect |
| 7. C89×#1343 | C2 | semidirect |
| 8. C2×#15667999 | C4 | semidirect |
| 13. #19151511 | C4 | semidirect |
| 16. #19151506 | C4 | semidirect |
| 19. #19151465 | C4 | semidirect |
| 227. #1343 | D89 | semidirect |
| 228. C89 | #11825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026109 | 2 |
| #26020239 | 2 |
| #26018587 | 2 |
| #26018274 | 2 |
| #26018272 | 2 |
| #26018249 | 2 |
| C89×#1343 | 2 |
| #11825 | 89 |