Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 133 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. #28409867 | C2 | semidirect |
| 2. #28409538 | C2 | semidirect |
| 3. #28409223 | C2 | semidirect |
| 4. #28409222 | C2 | semidirect |
| 5. #28409218 | C2 | semidirect |
| 6. #28409004 | C2 | semidirect |
| 7. B(4,𝔽2)×C227 | C2 | semidirect |
| 14. C23×Dic227 | C22 | semidirect |
| 15. #20300272 | C22 | semidirect |
| 16. #20300269 | C22 | semidirect |
| 19. #20300257 | C22 | semidirect |
| 22. #20300244 | C22 | semidirect |
| 23. #20300203 | C22 | semidirect |
| 24. #20300202 | C22 | semidirect |
| 26. #120×C227 | C22 | semidirect |
| 27. #99×C227 | C22 | semidirect |
| 37. C2×Dic454 | D4 | semidirect |
| 42. C2×C22⋊D227 | D4 | semidirect |
| 49. C22×Dic227 | D4 | semidirect |
| 53. C2×C4×D227 | D4 | semidirect |
| 126. C227 | #3025 | semidirect |
| 133. B(4,𝔽2) | D227 | semidirect |
| 148. #120 | C2×D227 | semidirect |
| 154. #99 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409867 | 2 |
| #28409538 | 2 |
| #28409223 | 2 |
| #28409222 | 2 |
| #28409218 | 2 |
| #28409004 | 2 |
| B(4,𝔽2)×C227 | 2 |
| #3025 | 227 |