Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1602 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 275 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. #26020328 | C2 | semidirect |
| 4. #26020326 | C2 | semidirect |
| 5. #26020324 | C2 | semidirect |
| 6. #342×D89 | C2 | semidirect |
| 7. C89×#1819 | C2 | semidirect |
| 10. C2×C4×C22⋊D89 | C4 | semidirect |
| 11. C2×#15667972 | C4 | semidirect |
| 29. C23×Dic89 | C2×C4 | semidirect |
| 37. C2×#13083553 | C2×C4 | semidirect |
| 40. C2×C22⋊Dic89 | C2×C4 | semidirect |
| 47. C2×C4×Dic89 | C2×C4 | semidirect |
| 50. C23×C4×C89 | C2×C4 | semidirect |
| 53. C2×C22⋊C4×C89 | C2×C4 | semidirect |
| 176. #1819 | D89 | semidirect |
| 178. C89 | #20689 | semidirect |
| 205. C23×C4 | C4×D89 | semidirect |
| 222. C2×C22⋊C4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152071 | 2 |
| #26022828 | 2 |
| #26020328 | 2 |
| #26020326 | 2 |
| #26020324 | 2 |
| #342×D89 | 2 |
| C89×#1819 | 2 |
| #20689 | 89 |