Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #26040010 | C2 | semidirect |
| 2. #26040008 | C2 | semidirect |
| 3. #26040005 | C2 | semidirect |
| 4. #26040001 | C2 | semidirect |
| 5. #26040000 | C2 | semidirect |
| 6. #26039997 | C2 | semidirect |
| 7. #26039993 | C2 | semidirect |
| 9. C4×Dic718 | C2 | semidirect |
| 10. C4×D1436 | C2 | semidirect |
| 11. C4×C22⋊D359 | C2 | semidirect |
| 12. C4×C22⋊D359 | C2 | semidirect |
| 13. #26039972 | C2 | semidirect |
| 14. C42×D359 | C2 | semidirect |
| 15. #117×C359 | C2 | semidirect |
| 103. C359 | #529 | semidirect |
| 118. #117 | D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040010 | 2 |
| #26040008 | 2 |
| #26040005 | 2 |
| #26040001 | 2 |
| #26040000 | 2 |
| #26039997 | 2 |
| #26039993 | 2 |
| #26039988 | 2 |
| C4×Dic718 | 2 |
| C4×D1436 | 2 |
| C4×C22⋊D359 | 2 |
| #26039972 | 2 |
| C42×D359 | 2 |
| #117×C359 | 2 |
| #529 | 359 |