Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26018276 | C2 | semidirect |
| 4. #26018252 | C2 | semidirect |
| 13. C2×#117×C89 | C4 | semidirect |
| 14. #400×C89 | C4 | semidirect |
| 16. #398×C89 | C4 | semidirect |
| 22. C4×C22⋊C4×C89 | C4 | semidirect |
| 181. C89 | #11727 | semidirect |
| 183. C2×#117 | Dic89 | semidirect |
| 186. #400 | Dic89 | semidirect |
| 188. #398 | Dic89 | semidirect |
| 195. C4×C22⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667927 | 2 |
| #26018573 | 2 |
| #26018276 | 2 |
| #26018252 | 2 |
| C89×#2395 | 2 |
| #11727 | 89 |