Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022139 | C2 | semidirect |
| 3. #26018457 | C2 | semidirect |
| 4. #26018442 | C2 | semidirect |
| 5. #26018438 | C2 | semidirect |
| 6. #26018388 | C2 | semidirect |
| 7. C89×#2177 | C2 | semidirect |
| 10. #19151436 | C4 | semidirect |
| 11. #19151433 | C4 | semidirect |
| 23. Dic712 | C2×C4 | semidirect |
| 25. D1424 | C2×C4 | semidirect |
| 29. #15667918 | C2×C4 | semidirect |
| 90. #2177 | D89 | semidirect |
| 95. C89 | #13658 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022565 | 2 |
| #26022139 | 2 |
| #26018457 | 2 |
| #26018442 | 2 |
| #26018438 | 2 |
| #26018388 | 2 |
| C89×#2177 | 2 |
| #13658 | 89 |