Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
394 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 1. #26022025 | C2 | semidirect |
| 3. #26021972 | C2 | semidirect |
| 4. #26021856 | C2 | semidirect |
| 5. #26021168 | C2 | semidirect |
| 24. C2×Q32×C89 | C4 | semidirect |
| 25. C2×SD32×C89 | C4 | semidirect |
| 170. C89 | #13248 | semidirect |
| 175. C2×Q32 | Dic89 | semidirect |
| 176. C2×SD32 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022025 | 2 |
| #26021980 | 2 |
| #26021972 | 2 |
| #26021856 | 2 |
| #26021168 | 2 |
| #26021151 | 2 |
| C2×#510×C89 | 2 |
| #13248 | 89 |