Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
670 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #26018377 | C2 | semidirect |
| 4. #26018376 | C2 | semidirect |
| 5. C89×#1393 | C2 | semidirect |
| 7. C2×#15667970 | C4 | semidirect |
| 8. C2×C42×D89 | C4 | semidirect |
| 11. #19151504 | C4 | semidirect |
| 12. #19151503 | C4 | semidirect |
| 192. #1393 | D89 | semidirect |
| 193. C89 | #12857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022739 | 2 |
| #26020168 | 2 |
| #26018377 | 2 |
| #26018376 | 2 |
| C89×#1393 | 2 |
| #12857 | 89 |