Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22576191 | C2 | semidirect |
| 2. C22×#16864641 | C2 | semidirect |
| 4. #31774119 | C2 | semidirect |
| 5. #31774097 | C2 | semidirect |
| 6. #31773924 | C2 | semidirect |
| 7. #31773901 | C2 | semidirect |
| 8. #31773891 | C2 | semidirect |
| 9. #519×C271 | C2 | semidirect |
| 13. C2×#16864644 | C22 | semidirect |
| 16. C2×#16864641 | C22 | semidirect |
| 23. C4⋊(C271⋊C8) | C22 | semidirect |
| 24. #22576083 | C22 | semidirect |
| 26. #22576080 | C22 | semidirect |
| 29. C4×Q8×C271 | C22 | semidirect |
| 55. C2×Q8×C271 | D4 | semidirect |
| 116. C271 | #3043 | semidirect |
| 121. #519 | D271 | semidirect |
| 142. C4×Q8 | C2×D271 | semidirect |
| 156. C2×Q8 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576191 | 2 |
| C22×#16864641 | 2 |
| #31774466 | 2 |
| #31774119 | 2 |
| #31774097 | 2 |
| #31773924 | 2 |
| #31773901 | 2 |
| #31773891 | 2 |
| #519×C271 | 2 |
| #3043 | 271 |