Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
440 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 143 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. #31774450 | C2 | semidirect |
| 3. #31774199 | C2 | semidirect |
| 4. #31774195 | C2 | semidirect |
| 5. #31774185 | C2 | semidirect |
| 6. #31774175 | C2 | semidirect |
| 7. #31773940 | C2 | semidirect |
| 8. #31773939 | C2 | semidirect |
| 9. #31773920 | C2 | semidirect |
| 14. #22576159 | C22 | semidirect |
| 15. #22576159 | C22 | semidirect |
| 16. #22576151 | C22 | semidirect |
| 17. #22576151 | C22 | semidirect |
| 30. #22576094 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. #22576092 | C22 | semidirect |
| 33. #22576091 | C22 | semidirect |
| 34. Dic271⋊C8 | C22 | semidirect |
| 35. Dic271⋊C8 | C22 | semidirect |
| 74. C2×D4×C271 | Q8 | semidirect |
| 138. C271 | #3077 | semidirect |
| 187. C2×D4 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774450 | 2 |
| C2×D4×Dic271 | 2 |
| #31774199 | 2 |
| #31774195 | 2 |
| #31774185 | 2 |
| #31774175 | 2 |
| #31773940 | 2 |
| #31773939 | 2 |
| #31773920 | 2 |
| #31773902 | 2 |
| #418×C271 | 2 |
| #3077 | 271 |