Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #26022025 | C2 | semidirect |
| 3. #26021981 | C2 | semidirect |
| 4. #26021969 | C2 | semidirect |
| 5. #26021162 | C2 | semidirect |
| 6. #26021150 | C2 | semidirect |
| 7. C89×#2110 | C2 | semidirect |
| 12. C2×#15667957 | C4 | semidirect |
| 13. C2×D1424 | C4 | semidirect |
| 172. #2110 | D89 | semidirect |
| 175. C89 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| #26022025 | 2 |
| #26021981 | 2 |
| #26021969 | 2 |
| #26021162 | 2 |
| #26021150 | 2 |
| C89×#2110 | 2 |
| #13247 | 89 |