Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26021861 | C2 | semidirect |
| 3. C22⋊C16×D89 | C2 | semidirect |
| 4. #26018191 | C2 | semidirect |
| 5. #26018191 | C2 | semidirect |
| 6. #26018176 | C2 | semidirect |
| 7. C89×#1314 | C2 | semidirect |
| 196. #1314 | D89 | semidirect |
| 197. C89 | #11467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151672 | 2 |
| #26021861 | 2 |
| C22⋊C16×D89 | 2 |
| #26018191 | 2 |
| #26018176 | 2 |
| C89×#1314 | 2 |
| #11467 | 89 |