Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C2×#19151636 | C2 | semidirect |
| 2. C2×#19151408 | C2 | semidirect |
| 3. #26021863 | C2 | semidirect |
| 4. #26018357 | C2 | semidirect |
| 16. #467×C89 | C4 | semidirect |
| 17. #466×C89 | C4 | semidirect |
| 31. #15667944 | D4 | semidirect |
| 163. C89 | #13002 | semidirect |
| 169. #467 | Dic89 | semidirect |
| 170. #466 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151636 | 2 |
| C2×#19151408 | 2 |
| #26021863 | 2 |
| #26018357 | 2 |
| C89×#3050 | 2 |
| #13002 | 89 |