Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
584 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 7. #19151393 | C4 | direct (N × H) |
| 10. C2×C4×Q8×C89 | C4 | semidirect |
| 12. #391×C89 | C4 | semidirect |
| 15. #382×C89 | C4 | semidirect |
| 17. C43×C89 | C4 | semidirect |
| 54. C2×Q8×C89 | C42 | semidirect |
| 84. C42×C89 | C42 | semidirect |
| 141. C4×C89 | #354 | semidirect |
| 154. C89 | C4×#354 | semidirect |
| 156. C2×C4×Q8 | Dic89 | semidirect |
| 159. #391 | Dic89 | semidirect |
| 162. #382 | Dic89 | semidirect |
| 165. C43 | Dic89 | semidirect |
| 200. C2×Q8 | C4×Dic89 | semidirect |
| 234. C42 | C4×Dic89 | semidirect |
| 292. C4 | #19151393 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151393 | 2 |
| C4×#15667927 | 2 |
| #26018377 | 2 |
| C4×#124×C89 | 2 |
| C4×#354 | 89 |