Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
720 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 115 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. #99×Dic89 | C2 | semidirect |
| 4. #26018377 | C2 | semidirect |
| 5. C89×#1393 | C2 | semidirect |
| 8. C2×#15667974 | C4 | semidirect |
| 11. #19151500 | C4 | semidirect |
| 13. #19151467 | C4 | semidirect |
| 15. C42×Dic89 | C4 | semidirect |
| 16. #19151390 | C4 | semidirect |
| 44. #15667927 | C2×C4 | semidirect |
| 52. #99×C89 | C2×C4 | semidirect |
| 57. C2×D356 | C42 | semidirect |
| 86. C4×Dic89 | C42 | semidirect |
| 177. Dic89 | #353 | semidirect |
| 191. #1393 | D89 | semidirect |
| 192. C89 | C4×#353 | semidirect |
| 238. #99 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022816 | 2 |
| C2×#19151390 | 2 |
| #99×Dic89 | 2 |
| #26018377 | 2 |
| C89×#1393 | 2 |
| C4×#353 | 89 |