Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
426 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19151427 | C2 | semidirect |
| 3. C2×#19151406 | C2 | semidirect |
| 4. C2×C16×Dic89 | C2 | semidirect |
| 5. #26021141 | C2 | semidirect |
| 6. #26021138 | C2 | semidirect |
| 7. C2×#359×C89 | C2 | semidirect |
| 11. C2×#15667958 | C4 | semidirect |
| 12. C2×#15667956 | C4 | semidirect |
| 13. C2×#15667955 | C4 | semidirect |
| 14. C2×#15667953 | C4 | semidirect |
| 182. C2×#359 | D89 | semidirect |
| 186. C89 | #13241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152028 | 2 |
| C2×#19151427 | 2 |
| C2×#19151406 | 2 |
| C2×C16×Dic89 | 2 |
| #26021141 | 2 |
| #26021138 | 2 |
| C2×#359×C89 | 2 |
| #13241 | 89 |