Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
612 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 3. #26018165 | C2 | semidirect |
| 4. #26018165 | C2 | semidirect |
| 5. C89×#1309 | C2 | semidirect |
| 138. #1309 | D89 | semidirect |
| 139. C89 | #8129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028884 | 2 |
| #423×D89 | 2 |
| #26018165 | 2 |
| C89×#1309 | 2 |
| #8129 | 89 |