Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #28409511 | C2 | semidirect |
| 3. #28409144 | C2 | semidirect |
| 4. #28409140 | C2 | semidirect |
| 5. #28409138 | C2 | semidirect |
| 6. #28409123 | C2 | semidirect |
| 7. C4×#16813872 | C2 | semidirect |
| 8. #106×D227 | C2 | semidirect |
| 9. #28409030 | C2 | semidirect |
| 10. #28408989 | C2 | semidirect |
| 11. #442×C227 | C2 | semidirect |
| 13. #20300307 | C4 | semidirect |
| 41. #16813883 | C2×C4 | semidirect |
| 48. Dic908 | C2×C4 | semidirect |
| 49. #16813872 | C2×C4 | semidirect |
| 53. C8×D227 | C2×C4 | semidirect |
| 66. D8×C227 | C2×C4 | semidirect |
| 114. C227 | #2952 | semidirect |
| 119. #442 | D227 | semidirect |
| 167. D8 | C4×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300307 | 2 |
| #28409511 | 2 |
| #28409144 | 2 |
| #28409140 | 2 |
| #28409138 | 2 |
| #28409123 | 2 |
| C4×#16813872 | 2 |
| #106×D227 | 2 |
| #28409030 | 2 |
| #28408989 | 2 |
| #442×C227 | 2 |
| #2952 | 227 |