Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774452 | C2 | semidirect |
| 3. #31774234 | C2 | semidirect |
| 4. #31774174 | C2 | semidirect |
| 5. #31774103 | C2 | semidirect |
| 6. #31774102 | C2 | semidirect |
| 8. #31773996 | C2 | semidirect |
| 9. #31773994 | C2 | semidirect |
| 10. #31773953 | C2 | semidirect |
| 11. #474×C271 | C2 | semidirect |
| 16. #22576160 | C22 | semidirect |
| 21. #22576125 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. C4⋊(C271⋊C8) | C22 | semidirect |
| 33. #22576085 | C22 | semidirect |
| 34. #22576083 | C22 | semidirect |
| 37. #22576070 | C22 | semidirect |
| 38. C4⋊Q8×C271 | C22 | semidirect |
| 40. #107×C271 | C22 | semidirect |
| 41. C4⋊C8×C271 | C22 | semidirect |
| 146. C271 | #3110 | semidirect |
| 152. #474 | D271 | semidirect |
| 164. C4⋊Q8 | C2×D271 | semidirect |
| 181. #107 | C2×D271 | semidirect |
| 183. C4⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4×D4×D271 | 2 |
| #31774234 | 2 |
| #31774174 | 2 |
| #31774103 | 2 |
| #31774102 | 2 |
| #31774049 | 2 |
| #31773996 | 2 |
| #31773994 | 2 |
| #31773953 | 2 |
| #474×C271 | 2 |
| #3110 | 271 |