Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
| 4. #26021001 | C2 | semidirect |
| 5. #26018353 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 25. #360×C89 | C4 | semidirect |
| 58. M32×C89 | C2×C4 | semidirect |
| 61. #106×C89 | C2×C4 | semidirect |
| 162. C89 | #12951 | semidirect |
| 179. #360 | Dic89 | semidirect |
| 203. M32 | C2×Dic89 | semidirect |
| 211. #106 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×Dic89 | 2 |
| #26022025 | 2 |
| #26022001 | 2 |
| #26021001 | 2 |
| #26018353 | 2 |
| #26018333 | 2 |
| C89×#2145 | 2 |
| #12951 | 89 |