Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
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. #31774376 | C2 | semidirect |
| 3. #31774009 | C2 | semidirect |
| 4. #31774005 | C2 | semidirect |
| 5. #31774003 | C2 | semidirect |
| 6. #31773988 | C2 | semidirect |
| 7. C4×#16864642 | C2 | semidirect |
| 8. #106×D271 | C2 | semidirect |
| 9. #31773895 | C2 | semidirect |
| 10. #31773854 | C2 | semidirect |
| 11. #442×C271 | C2 | semidirect |
| 13. #22576179 | C4 | semidirect |
| 41. #16864653 | C2×C4 | semidirect |
| 48. Dic1084 | C2×C4 | semidirect |
| 49. #16864642 | C2×C4 | semidirect |
| 53. C8×D271 | C2×C4 | semidirect |
| 66. D8×C271 | C2×C4 | semidirect |
| 114. C271 | #2952 | semidirect |
| 119. #442 | D271 | semidirect |
| 167. D8 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576179 | 2 |
| #31774376 | 2 |
| #31774009 | 2 |
| #31774005 | 2 |
| #31774003 | 2 |
| #31773988 | 2 |
| C4×#16864642 | 2 |
| #106×D271 | 2 |
| #31773895 | 2 |
| #31773854 | 2 |
| #442×C271 | 2 |
| #2952 | 271 |