Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #28409506 | C2 | semidirect |
| 3. #28409142 | C2 | semidirect |
| 4. C4×#16813869 | C2 | semidirect |
| 5. #28409068 | C2 | semidirect |
| 6. #28409037 | C2 | semidirect |
| 7. #28409036 | C2 | semidirect |
| 8. #28408988 | C2 | semidirect |
| 9. #518×C227 | C2 | semidirect |
| 11. C2×#16813869 | C4 | semidirect |
| 16. C4×D908 | C22 | semidirect |
| 20. #20300221 | C22 | semidirect |
| 21. #20300219 | C22 | semidirect |
| 22. #20300209 | C22 | semidirect |
| 23. #20300208 | C22 | semidirect |
| 24. #20300199 | C22 | semidirect |
| 25. C4×C227⋊C8 | C22 | semidirect |
| 28. C4×D4×C227 | C22 | semidirect |
| 35. C2×D908 | C2×C4 | semidirect |
| 38. #16813869 | C2×C4 | semidirect |
| 39. #16813869 | C2×C4 | semidirect |
| 41. C2×C227⋊C8 | C2×C4 | semidirect |
| 52. C2×D4×C227 | C2×C4 | semidirect |
| 108. C227 | #2948 | semidirect |
| 112. #518 | D227 | semidirect |
| 129. C4×D4 | C2×D227 | semidirect |
| 149. C2×D4 | C4×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813869 | 2 |
| #28409506 | 2 |
| #28409142 | 2 |
| C4×#16813869 | 2 |
| #28409068 | 2 |
| #28409037 | 2 |
| #28409036 | 2 |
| #28408988 | 2 |
| #518×C227 | 2 |
| #2948 | 227 |