Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1068 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26020195 | C2 | semidirect |
| 3. C4×#15667927 | C2 | semidirect |
| 4. #26018773 | C2 | semidirect |
| 5. C89×#1465 | C2 | semidirect |
| 7. C23×Dic178 | C4 | semidirect |
| 10. C2×#15668000 | C4 | semidirect |
| 14. C2×#15667986 | C4 | semidirect |
| 16. C2×C4×Dic178 | C4 | semidirect |
| 152. C23×C89 | #104 | semidirect |
| 198. Dic178 | #99 | semidirect |
| 243. #1465 | D89 | semidirect |
| 244. C89 | #8366 | semidirect |
| 396. C23 | #15667938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152257 | 2 |
| #26020195 | 2 |
| C4×#15667927 | 2 |
| #26018773 | 2 |
| C89×#1465 | 2 |
| #8366 | 89 |