Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 1. #26022055 | C2 | semidirect |
| 2. C4×#15667944 | C2 | semidirect |
| 3. #26018261 | C2 | semidirect |
| 12. #500×C89 | C4 | semidirect |
| 13. #493×C89 | C4 | semidirect |
| 18. C4×D8×C89 | C4 | semidirect |
| 130. C89 | #11744 | semidirect |
| 132. #500 | Dic89 | semidirect |
| 133. #493 | Dic89 | semidirect |
| 138. C4×D8 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022055 | 2 |
| C4×#15667944 | 2 |
| #26018261 | 2 |
| C89×#3169 | 2 |
| #11744 | 89 |