Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#22576207 | C2 | semidirect |
| 2. C2×#22576188 | C2 | semidirect |
| 3. C22×#16864643 | C2 | semidirect |
| 4. #31774461 | C2 | semidirect |
| 5. #31774044 | C2 | semidirect |
| 6. #31774038 | C2 | semidirect |
| 7. #31773907 | C2 | semidirect |
| 8. #31773894 | C2 | semidirect |
| 9. #408×C271 | C2 | semidirect |
| 13. C2×#16864654 | C22 | semidirect |
| 17. C22×Dic542 | C22 | semidirect |
| 30. #22576085 | C22 | semidirect |
| 31. #22576085 | C22 | semidirect |
| 32. #22576082 | C22 | semidirect |
| 36. C22⋊C8×C271 | C22 | semidirect |
| 41. #16864654 | D4 | semidirect |
| 49. C2×Dic542 | D4 | semidirect |
| 145. C271 | #3010 | semidirect |
| 155. #408 | D271 | semidirect |
| 182. C22⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576207 | 2 |
| C2×#22576188 | 2 |
| C22×#16864643 | 2 |
| #31774461 | 2 |
| #31774044 | 2 |
| #31774038 | 2 |
| #31773907 | 2 |
| #31773894 | 2 |
| #408×C271 | 2 |
| #3010 | 271 |