Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
484 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 109 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. #135×Dic89 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. #26021138 | C2 | semidirect |
| 5. #26018366 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 7. C89×#2143 | C2 | semidirect |
| 11. #19152038 | C4 | semidirect |
| 13. #19152033 | C4 | semidirect |
| 34. C2×Dic356 | C2×C4 | semidirect |
| 36. C2×D712 | C2×C4 | semidirect |
| 50. #15667952 | C2×C4 | semidirect |
| 195. #2143 | D89 | semidirect |
| 199. C89 | #13027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #135×Dic89 | 2 |
| #26021989 | 2 |
| #26021138 | 2 |
| #26018366 | 2 |
| #26018333 | 2 |
| C89×#2143 | 2 |
| #13027 | 89 |