Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
926 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 926 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. C2×#19151412 | C2 | semidirect |
| 3. #26021981 | C2 | semidirect |
| 4. #26020302 | C2 | semidirect |
| 5. C89×#2115 | C2 | semidirect |
| 15. C2×#15667948 | C22 | semidirect |
| 21. C2×M32×C89 | C22 | semidirect |
| 178. #2115 | D89 | semidirect |
| 180. C89 | #12743 | semidirect |
| 191. C2×M32 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152403 | 2 |
| C2×#19151412 | 2 |
| #26021981 | 2 |
| #26020302 | 2 |
| C89×#2115 | 2 |
| #12743 | 89 |