Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22576182 | C2 | semidirect |
| 2. C22×#16864637 | C2 | semidirect |
| 3. #31774409 | C2 | semidirect |
| 4. #31774156 | C2 | semidirect |
| 5. #31774151 | C2 | semidirect |
| 6. #31774144 | C2 | semidirect |
| 7. #31773891 | C2 | semidirect |
| 8. #427×C271 | C2 | semidirect |
| 12. C2×Dic1084 | C22 | semidirect |
| 13. C2×#16864643 | C22 | semidirect |
| 14. C2×D2168 | C22 | semidirect |
| 24. #22576083 | C22 | semidirect |
| 25. #22576080 | C22 | semidirect |
| 28. #107×C271 | C22 | semidirect |
| 29. #106×C271 | C22 | semidirect |
| 54. C2×C8×C271 | D4 | semidirect |
| 105. C271 | #3054 | semidirect |
| 113. #427 | D271 | semidirect |
| 132. #107 | C2×D271 | semidirect |
| 133. #106 | C2×D271 | semidirect |
| 157. C2×C8 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576182 | 2 |
| C22×#16864637 | 2 |
| #31774409 | 2 |
| #31774156 | 2 |
| #31774151 | 2 |
| #31774144 | 2 |
| #31773891 | 2 |
| #427×C271 | 2 |
| #3054 | 271 |