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. #28409514 | C2 | semidirect |
| 3. #28409145 | C2 | semidirect |
| 4. #28409143 | C2 | semidirect |
| 5. #28409139 | C2 | semidirect |
| 6. C4×#16813871 | C2 | semidirect |
| 7. #28409117 | C2 | semidirect |
| 8. #106×D227 | C2 | semidirect |
| 9. #28409032 | C2 | semidirect |
| 10. #28408989 | C2 | semidirect |
| 11. #441×C227 | C2 | semidirect |
| 13. #20300311 | C4 | semidirect |
| 41. #16813885 | C2×C4 | semidirect |
| 49. #16813871 | C2×C4 | semidirect |
| 50. D1816 | C2×C4 | semidirect |
| 54. C8×D227 | C2×C4 | semidirect |
| 65. Q16×C227 | C2×C4 | semidirect |
| 114. C227 | #2952 | semidirect |
| 121. #441 | D227 | semidirect |
| 165. Q16 | C4×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300311 | 2 |
| #28409514 | 2 |
| #28409145 | 2 |
| #28409143 | 2 |
| #28409139 | 2 |
| C4×#16813871 | 2 |
| #28409117 | 2 |
| #106×D227 | 2 |
| #28409032 | 2 |
| #28408989 | 2 |
| #441×C227 | 2 |
| #2952 | 227 |