Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31774696 | C2 | semidirect |
| 2. C2×#22576183 | C2 | semidirect |
| 3. #131×D271 | C2 | semidirect |
| 4. #31774169 | C2 | semidirect |
| 5. #31774168 | C2 | semidirect |
| 6. #31774167 | C2 | semidirect |
| 7. #31774163 | C2 | semidirect |
| 8. #31774162 | C2 | semidirect |
| 9. #108×D271 | C2 | semidirect |
| 10. #31773880 | C2 | semidirect |
| 11. #473×C271 | C2 | semidirect |
| 25. C2×#16864641 | C22 | semidirect |
| 26. C2×D2168 | C22 | semidirect |
| 37. #22576096 | C22 | semidirect |
| 38. #22576095 | C22 | semidirect |
| 39. #22576079 | C22 | semidirect |
| 40. #22576076 | C22 | semidirect |
| 41. #22576076 | C22 | semidirect |
| 43. C2×Q16×C271 | C22 | semidirect |
| 45. #108×C271 | C22 | semidirect |
| 46. #101×C271 | C22 | semidirect |
| 166. C271 | #3067 | semidirect |
| 172. #473 | D271 | semidirect |
| 193. C2×Q16 | C2×D271 | semidirect |
| 209. #108 | C2×D271 | semidirect |
| 211. #101 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774696 | 2 |
| C2×#22576183 | 2 |
| #131×D271 | 2 |
| #31774169 | 2 |
| #31774168 | 2 |
| #31774167 | 2 |
| #31774163 | 2 |
| #31774162 | 2 |
| #108×D271 | 2 |
| #31773880 | 2 |
| #473×C271 | 2 |
| #3067 | 271 |