Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
960 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26021066 | C2 | semidirect |
| 3. C2×#19151338 | C2 | semidirect |
| 4. C2×#19151337 | C2 | semidirect |
| 5. C89×#1959 | C2 | semidirect |
| 8. #19152340 | C4 | semidirect |
| 16. C2×#15667923 | C22 | semidirect |
| 22. C2×#97×C89 | C22 | semidirect |
| 23. #384×C89 | C22 | semidirect |
| 201. #1959 | D89 | semidirect |
| 204. C89 | #8506 | semidirect |
| 219. C2×#97 | C2×D89 | semidirect |
| 220. #384 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152340 | 2 |
| #26021066 | 2 |
| C2×#19151338 | 2 |
| C2×#19151337 | 2 |
| C89×#1959 | 2 |
| #8506 | 89 |