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. #31774693 | C2 | semidirect |
| 2. C2×#22576179 | C2 | semidirect |
| 3. #131×D271 | C2 | semidirect |
| 4. #31774173 | C2 | semidirect |
| 5. #31774172 | C2 | semidirect |
| 6. #31774164 | C2 | semidirect |
| 7. #31774159 | C2 | semidirect |
| 8. #31774158 | C2 | semidirect |
| 9. #108×D271 | C2 | semidirect |
| 10. #31773878 | C2 | semidirect |
| 11. #472×C271 | C2 | semidirect |
| 25. C2×Dic1084 | C22 | semidirect |
| 26. C2×#16864642 | C22 | semidirect |
| 37. #22576096 | C22 | semidirect |
| 38. #22576095 | C22 | semidirect |
| 39. #22576078 | C22 | semidirect |
| 40. #22576078 | C22 | semidirect |
| 41. #22576077 | C22 | semidirect |
| 43. C2×D8×C271 | C22 | semidirect |
| 45. #108×C271 | C22 | semidirect |
| 46. #100×C271 | C22 | semidirect |
| 166. C271 | #3067 | semidirect |
| 174. #472 | D271 | semidirect |
| 195. C2×D8 | C2×D271 | semidirect |
| 209. #108 | C2×D271 | semidirect |
| 213. #100 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774693 | 2 |
| C2×#22576179 | 2 |
| #131×D271 | 2 |
| #31774173 | 2 |
| #31774172 | 2 |
| #31774164 | 2 |
| #31774159 | 2 |
| #31774158 | 2 |
| #108×D271 | 2 |
| #31773878 | 2 |
| #472×C271 | 2 |
| #3067 | 271 |