Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
374 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26022505 | C2 | semidirect |
| 3. #26022298 | C2 | semidirect |
| 4. #26019617 | C2 | semidirect |
| 5. #26018302 | C2 | semidirect |
| 6. #26018214 | C2 | semidirect |
| 7. C89×D4⋊C16 | C2 | semidirect |
| 150. D4⋊C16 | D89 | semidirect |
| 151. C89 | #12323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031974 | 2 |
| #26022505 | 2 |
| #26022298 | 2 |
| #26019617 | 2 |
| #26018302 | 2 |
| #26018214 | 2 |
| C89×D4⋊C16 | 2 |
| #12323 | 89 |