Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1060 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26020186 | C2 | semidirect |
| 3. #26018819 | C2 | semidirect |
| 4. #26018570 | C2 | semidirect |
| 5. C89×#1799 | C2 | semidirect |
| 6. C22×#13083574 | C4 | semidirect |
| 10. C2×#15668000 | C4 | semidirect |
| 12. C2×#15667991 | C4 | semidirect |
| 16. C2×C4×Dic178 | C4 | semidirect |
| 203. Dic178 | #99 | semidirect |
| 248. #1799 | D89 | semidirect |
| 252. C89 | #8377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152257 | 2 |
| #26020186 | 2 |
| #26018819 | 2 |
| #26018570 | 2 |
| C89×#1799 | 2 |
| #8377 | 89 |