Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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. #31774196 | C2 | semidirect |
| 4. #31774195 | C2 | semidirect |
| 5. #31774184 | C2 | semidirect |
| 6. #31774178 | C2 | semidirect |
| 7. #31774177 | C2 | semidirect |
| 8. #31773936 | C2 | semidirect |
| 9. #31773919 | C2 | semidirect |
| 11. #476×C271 | C2 | semidirect |
| 15. #22576160 | C22 | semidirect |
| 16. #22576151 | C22 | semidirect |
| 30. #22576094 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. #22576091 | C22 | semidirect |
| 33. C4⋊(C271⋊C8) | C22 | semidirect |
| 34. Dic271⋊C8 | C22 | semidirect |
| 38. C4⋊Q8×C271 | C22 | semidirect |
| 40. #106×C271 | C22 | semidirect |
| 41. C4⋊C8×C271 | C22 | semidirect |
| 48. D4×D271 | Q8 | semidirect |
| 144. C271 | #3077 | semidirect |
| 151. #476 | D271 | semidirect |
| 161. C4⋊Q8 | C2×D271 | semidirect |
| 180. #106 | 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 |
| #31774196 | 2 |
| #31774195 | 2 |
| #31774184 | 2 |
| #31774178 | 2 |
| #31774177 | 2 |
| #31773936 | 2 |
| #31773919 | 2 |
| #31773900 | 2 |
| #476×C271 | 2 |
| #3077 | 271 |