Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#16864643 | C2 | semidirect |
| 2. C2×#22576166 | C2 | semidirect |
| 3. #31774473 | C2 | semidirect |
| 5. #31774144 | C2 | semidirect |
| 6. #31774127 | C2 | semidirect |
| 7. #31773905 | C2 | semidirect |
| 8. #31773901 | C2 | semidirect |
| 9. #427×C271 | C2 | semidirect |
| 18. C2×#16864637 | C22 | semidirect |
| 19. C2×C8×D271 | C22 | semidirect |
| 25. #22576140 | C22 | semidirect |
| 28. #22576083 | C22 | semidirect |
| 33. #107×C271 | C22 | semidirect |
| 34. #106×C271 | C22 | semidirect |
| 62. C2×C8×C271 | D4 | semidirect |
| 120. C271 | #3057 | semidirect |
| 128. #427 | D271 | semidirect |
| 152. #107 | C2×D271 | semidirect |
| 153. #106 | C2×D271 | semidirect |
| 180. C2×C8 | D1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864643 | 2 |
| C2×#22576166 | 2 |
| #31774473 | 2 |
| #31774466 | 2 |
| #31774144 | 2 |
| #31774127 | 2 |
| #31773905 | 2 |
| #31773901 | 2 |
| #427×C271 | 2 |
| #3057 | 271 |