Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 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. #31774448 | C2 | semidirect |
| 2. C4×D4×D271 | C2 | semidirect |
| 3. #31774217 | C2 | semidirect |
| 4. #31774184 | C2 | semidirect |
| 5. #31774093 | C2 | semidirect |
| 6. #31774092 | C2 | semidirect |
| 7. #31774032 | C2 | semidirect |
| 8. #31774008 | C2 | semidirect |
| 9. #31774006 | C2 | semidirect |
| 10. #31773953 | C2 | semidirect |
| 11. #476×C271 | C2 | semidirect |
| 17. #22576157 | C22 | semidirect |
| 25. #22576122 | C22 | semidirect |
| 31. #22576091 | C22 | semidirect |
| 32. C4⋊(C271⋊C8) | C22 | semidirect |
| 33. #22576082 | C22 | semidirect |
| 35. #22576080 | C22 | semidirect |
| 37. #22576070 | C22 | semidirect |
| 38. C4⋊Q8×C271 | C22 | semidirect |
| 40. #106×C271 | C22 | semidirect |
| 41. C4⋊C8×C271 | C22 | semidirect |
| 96. D1084 | #41 | semidirect |
| 115. D4×C271 | #41 | semidirect |
| 154. C271 | #3109 | semidirect |
| 160. #476 | D271 | semidirect |
| 172. C4⋊Q8 | C2×D271 | semidirect |
| 189. #106 | C2×D271 | semidirect |
| 191. C4⋊C8 | C2×D271 | semidirect |
| 256. D4 | #16864655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774448 | 2 |
| C4×D4×D271 | 2 |
| #31774217 | 2 |
| #31774184 | 2 |
| #31774093 | 2 |
| #31774092 | 2 |
| #31774032 | 2 |
| #31774008 | 2 |
| #31774006 | 2 |
| #31773953 | 2 |
| #476×C271 | 2 |
| #3109 | 271 |