Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774714 | C2 | semidirect |
| 2. #31774702 | C2 | semidirect |
| 3. #31774340 | C2 | semidirect |
| 4. #31774335 | C2 | semidirect |
| 5. #31774329 | C2 | semidirect |
| 6. C2×#22576105 | C2 | semidirect |
| 7. #504×C271 | C2 | semidirect |
| 13. #22576182 | C22 | semidirect |
| 14. C2×Dic1084 | C22 | semidirect |
| 16. Dic2168 | C22 | semidirect |
| 17. #22576105 | C22 | semidirect |
| 18. #22576105 | C22 | semidirect |
| 19. #22576105 | C22 | semidirect |
| 20. D4336 | C22 | semidirect |
| 22. M32×C271 | C22 | semidirect |
| 23. C2×C16×C271 | C22 | semidirect |
| 74. C271 | #3416 | semidirect |
| 82. #504 | D271 | semidirect |
| 97. M32 | C2×D271 | semidirect |
| 98. C2×C16 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774714 | 2 |
| #31774702 | 2 |
| #31774340 | 2 |
| #31774335 | 2 |
| #31774329 | 2 |
| C2×#22576105 | 2 |
| #504×C271 | 2 |
| #3416 | 271 |