Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1200 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 1200 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. #26020182 | C2 | semidirect |
| 3. #26018823 | C2 | semidirect |
| 4. #26018570 | C2 | semidirect |
| 5. C89×#1799 | C2 | semidirect |
| 6. C22×#13083574 | C4 | semidirect |
| 10. C2×#15668000 | C4 | semidirect |
| 13. C2×#15667986 | C4 | semidirect |
| 16. C2×C4×D356 | C4 | semidirect |
| 210. D356 | #99 | semidirect |
| 266. #1799 | D89 | semidirect |
| 270. C89 | #8381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152244 | 2 |
| #26020182 | 2 |
| #26018823 | 2 |
| #26018570 | 2 |
| C89×#1799 | 2 |
| #8381 | 89 |