Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
720 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 139 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. C4×#15667927 | C2 | semidirect |
| 3. #26018377 | C2 | semidirect |
| 7. #19151391 | C4 | direct (N × H) |
| 11. C2×C4×D4×C89 | C4 | semidirect |
| 14. #390×C89 | C4 | semidirect |
| 16. #384×C89 | C4 | semidirect |
| 17. C43×C89 | C4 | semidirect |
| 21. #15667927 | C2×C4 | semidirect |
| 61. C2×D4×C89 | C42 | semidirect |
| 90. C42×C89 | C42 | semidirect |
| 156. C4×C89 | #353 | semidirect |
| 170. C89 | C4×#353 | semidirect |
| 173. C2×C4×D4 | Dic89 | semidirect |
| 177. #390 | Dic89 | semidirect |
| 179. #384 | Dic89 | semidirect |
| 181. C43 | Dic89 | semidirect |
| 223. C2×D4 | C4×Dic89 | semidirect |
| 256. C42 | C4×Dic89 | semidirect |
| 323. C4 | #19151391 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| C4×#15667927 | 2 |
| #26018377 | 2 |
| C4×#127×C89 | 2 |
| C4×#353 | 89 |