Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26030645 | C2 | semidirect |
| 3. #26026188 | C2 | semidirect |
| 4. #26018970 | C2 | semidirect |
| 5. #26018851 | C2 | semidirect |
| 6. #26018145 | C2 | semidirect |
| 7. C89×#1505 | C2 | semidirect |
| 193. #1505 | D89 | semidirect |
| 195. C89 | #10092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031235 | 2 |
| #26030645 | 2 |
| #26026188 | 2 |
| #26018970 | 2 |
| #26018851 | 2 |
| #26018145 | 2 |
| C89×#1505 | 2 |
| #10092 | 89 |