Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
322 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26022480 | C2 | semidirect |
| 4. #26019622 | C2 | semidirect |
| 5. #26018306 | C2 | semidirect |
| 7. C89×Q8⋊C16 | C2 | semidirect |
| 87. Q8×C89 | SD32 | semidirect |
| 135. Q8⋊C16 | D89 | semidirect |
| 137. C89 | #12356 | semidirect |
| 222. Q8 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D712 | 2 |
| #26022480 | 2 |
| #26022298 | 2 |
| #26019622 | 2 |
| #26018306 | 2 |
| #26018214 | 2 |
| C89×Q8⋊C16 | 2 |
| #12356 | 89 |