Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #31774433 | C2 | semidirect |
| 2. C2×#22576122 | C2 | semidirect |
| 3. #31774210 | C2 | semidirect |
| 4. #31774196 | C2 | semidirect |
| 5. #31774115 | C2 | semidirect |
| 6. #31774047 | C2 | semidirect |
| 8. #31774008 | C2 | semidirect |
| 9. #31774000 | C2 | semidirect |
| 10. #31773951 | C2 | semidirect |
| 11. #483×C271 | C2 | semidirect |
| 17. #22576151 | C22 | semidirect |
| 18. #22576149 | C22 | semidirect |
| 21. Q8×Dic271 | C22 | semidirect |
| 26. #22576122 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. Dic271⋊C8 | C22 | semidirect |
| 35. #22576080 | C22 | semidirect |
| 37. #22576070 | C22 | semidirect |
| 40. #106×C271 | C22 | semidirect |
| 41. #103×C271 | C22 | semidirect |
| 140. C271 | #3114 | semidirect |
| 144. #483 | D271 | semidirect |
| 175. #106 | C2×D271 | semidirect |
| 177. #103 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774433 | 2 |
| C2×#22576122 | 2 |
| #31774210 | 2 |
| #31774196 | 2 |
| #31774115 | 2 |
| #31774047 | 2 |
| #31774033 | 2 |
| #31774008 | 2 |
| #31774000 | 2 |
| #31773951 | 2 |
| #483×C271 | 2 |
| #3114 | 271 |