Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
594 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 594 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 |
|---|---|---|
| 2. C2×#19151324 | C2 | semidirect |
| 3. #26018185 | C2 | semidirect |
| 4. #26018183 | C2 | semidirect |
| 5. C2×#324×C89 | C2 | semidirect |
| 27. C2×#13083574 | C8 | semidirect |
| 68. C2×Dic178 | C2×C8 | semidirect |
| 72. C2×D356 | C2×C8 | semidirect |
| 213. C2×#324 | D89 | semidirect |
| 216. C89 | #11432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022845 | 2 |
| C2×#19151324 | 2 |
| #26018185 | 2 |
| #26018183 | 2 |
| C2×#324×C89 | 2 |
| #11432 | 89 |