Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. #28409130 | C2 | semidirect |
| 4. C4×#16813871 | C2 | semidirect |
| 5. #28409068 | C2 | semidirect |
| 6. #28409041 | C2 | semidirect |
| 8. #28408988 | C2 | semidirect |
| 9. #519×C227 | C2 | semidirect |
| 11. C2×#16813871 | C4 | semidirect |
| 20. #20300221 | C22 | semidirect |
| 21. #20300219 | C22 | semidirect |
| 22. #20300212 | C22 | semidirect |
| 24. #20300199 | C22 | semidirect |
| 25. C4×C227⋊C8 | C22 | semidirect |
| 28. C4×Q8×C227 | C22 | semidirect |
| 38. #16813871 | C2×C4 | semidirect |
| 39. #16813871 | C2×C4 | semidirect |
| 41. C2×C227⋊C8 | C2×C4 | semidirect |
| 51. C2×Q8×C227 | C2×C4 | semidirect |
| 103. C227 | #2949 | semidirect |
| 106. #519 | D227 | semidirect |
| 122. C4×Q8 | C2×D227 | semidirect |
| 139. C2×Q8 | C4×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813871 | 2 |
| #28409506 | 2 |
| #28409130 | 2 |
| C4×#16813871 | 2 |
| #28409068 | 2 |
| #28409041 | 2 |
| #28409036 | 2 |
| #28408988 | 2 |
| #519×C227 | 2 |
| #2949 | 227 |