Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #26021124 | C2 | semidirect |
| 5. #26018352 | C2 | semidirect |
| 6. #26018331 | C2 | semidirect |
| 7. C2×#362×C89 | C2 | semidirect |
| 12. C2×#15667958 | C4 | semidirect |
| 13. C2×#15667955 | C4 | semidirect |
| 172. C2×#362 | D89 | semidirect |
| 177. C89 | #13039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| C2×#19151719 | 2 |
| C2×#19151409 | 2 |
| #26021124 | 2 |
| #26018352 | 2 |
| #26018331 | 2 |
| C2×#362×C89 | 2 |
| #13039 | 89 |