Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
656 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26018106 | C2 | semidirect |
| 5. #26018105 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#1284 | C2 | semidirect |
| 9. C2×#15667969 | C4 | semidirect |
| 10. C2×C42×D89 | C4 | semidirect |
| 21. C4×#13083551 | C4 | semidirect |
| 22. C4×#13083551 | C4 | semidirect |
| 264. #1284 | D89 | semidirect |
| 265. C89 | #8738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022738 | 2 |
| #26020178 | 2 |
| #26020169 | 2 |
| #26018106 | 2 |
| #26018105 | 2 |
| #26018104 | 2 |
| C89×#1284 | 2 |
| #8738 | 89 |