Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
628 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 135 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 | semidirect |
| 10. C2×C4×D4×C89 | C4 | semidirect |
| 12. #390×C89 | C4 | semidirect |
| 16. #382×C89 | C4 | semidirect |
| 17. #376×C89 | C4 | semidirect |
| 21. #15667927 | C2×C4 | semidirect |
| 58. C2×D4×C89 | C42 | semidirect |
| 82. C42×C89 | C42 | semidirect |
| 159. C89 | #12628 | semidirect |
| 161. C2×C4×D4 | Dic89 | semidirect |
| 164. #390 | Dic89 | semidirect |
| 168. #382 | Dic89 | semidirect |
| 170. #376 | Dic89 | semidirect |
| 209. C2×D4 | C4×Dic89 | semidirect |
| 237. C42 | C4×Dic89 | semidirect |
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 |
| C89×#2328 | 2 |
| #12628 | 89 |