Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26020248 | C2 | semidirect |
| 3. #26019008 | C2 | semidirect |
| 6. #26018127 | C2 | semidirect |
| 7. C2×Q8⋊C8×C89 | C2 | semidirect |
| 194. C2×Q8⋊C8 | D89 | semidirect |
| 196. C89 | #10459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029724 | 2 |
| #26020248 | 2 |
| #26019008 | 2 |
| #26018927 | 2 |
| #26018704 | 2 |
| #26018127 | 2 |
| C2×Q8⋊C8×C89 | 2 |
| #10459 | 89 |