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. #26029381 | C2 | semidirect |
| 3. #26021080 | C2 | semidirect |
| 4. C4×#15667940 | C2 | semidirect |
| 5. #26018668 | C2 | semidirect |
| 6. #26018143 | C2 | semidirect |
| 7. C89×#1276 | C2 | semidirect |
| 11. #19151894 | C4 | semidirect |
| 12. #19151889 | C4 | semidirect |
| 13. #19151799 | C4 | semidirect |
| 14. #19151794 | C4 | semidirect |
| 179. Dic178 | #104 | semidirect |
| 223. #1276 | 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 |
|---|---|
| #26030313 | 2 |
| #26029381 | 2 |
| #26021080 | 2 |
| C4×#15667940 | 2 |
| #26018668 | 2 |
| #26018143 | 2 |
| C89×#1276 | 2 |
| #8970 | 89 |