Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26022395 | C2 | semidirect |
| 4. #26019646 | C2 | semidirect |
| 6. #26018217 | C2 | semidirect |
| 7. C89×Q8⋊C16 | C2 | semidirect |
| 134. Q8⋊C16 | D89 | semidirect |
| 136. C89 | #12381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033265 | 2 |
| #26022476 | 2 |
| #26022395 | 2 |
| #26019646 | 2 |
| #26018299 | 2 |
| #26018217 | 2 |
| C89×Q8⋊C16 | 2 |
| #12381 | 89 |