Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
514 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26029382 | C2 | semidirect |
| 3. C4×#15667940 | C2 | semidirect |
| 4. #26018669 | C2 | semidirect |
| 5. #26018141 | C2 | semidirect |
| 6. #26018085 | C2 | semidirect |
| 7. C89×#1962 | C2 | semidirect |
| 10. #19151890 | C4 | semidirect |
| 11. #19151885 | C4 | semidirect |
| 12. #19151795 | C4 | semidirect |
| 13. #19151790 | C4 | semidirect |
| 179. Dic178 | #104 | semidirect |
| 219. #1962 | D89 | semidirect |
| 224. C89 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030306 | 2 |
| #26029382 | 2 |
| C4×#15667940 | 2 |
| #26018669 | 2 |
| #26018141 | 2 |
| #26018085 | 2 |
| C89×#1962 | 2 |
| #8970 | 89 |