Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#22576179 | C2 | semidirect |
| 2. C2×M16×D271 | C2 | semidirect |
| 3. #31774407 | C2 | semidirect |
| 4. #31774156 | C2 | semidirect |
| 5. #31774155 | C2 | semidirect |
| 6. #31774147 | C2 | semidirect |
| 7. #31774142 | C2 | semidirect |
| 8. #31774141 | C2 | semidirect |
| 9. #31773932 | C2 | semidirect |
| 10. #31773890 | C2 | semidirect |
| 11. #469×C271 | C2 | semidirect |
| 15. C2×Dic1084 | C22 | semidirect |
| 16. C2×#16864642 | C22 | semidirect |
| 31. #22576093 | C22 | semidirect |
| 32. #22576092 | C22 | semidirect |
| 33. #22576085 | C22 | semidirect |
| 34. #22576083 | C22 | semidirect |
| 35. #22576081 | C22 | semidirect |
| 36. C2×D8×C271 | C22 | semidirect |
| 39. #106×C271 | C22 | semidirect |
| 40. #102×C271 | C22 | semidirect |
| 63. C8×D271 | D4 | semidirect |
| 140. C271 | #3054 | semidirect |
| 148. #469 | D271 | semidirect |
| 158. C2×D8 | C2×D271 | semidirect |
| 177. #106 | C2×D271 | semidirect |
| 181. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576179 | 2 |
| C2×M16×D271 | 2 |
| #31774407 | 2 |
| #31774156 | 2 |
| #31774155 | 2 |
| #31774147 | 2 |
| #31774142 | 2 |
| #31774141 | 2 |
| #31773932 | 2 |
| #31773890 | 2 |
| #469×C271 | 2 |
| #3054 | 271 |