Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D271 | C2 | semidirect |
| 2. C2×#22576192 | C2 | semidirect |
| 4. #31774052 | C2 | semidirect |
| 5. #31774051 | C2 | semidirect |
| 6. #31774038 | C2 | semidirect |
| 7. #31774037 | C2 | semidirect |
| 8. #31774036 | C2 | semidirect |
| 9. #31773904 | C2 | semidirect |
| 10. #31773859 | C2 | semidirect |
| 11. #451×C271 | C2 | semidirect |
| 23. C2×#16864644 | C22 | semidirect |
| 24. C2×#16864643 | C22 | semidirect |
| 25. C2×#16864641 | C22 | semidirect |
| 35. #22576085 | C22 | semidirect |
| 36. #22576084 | C22 | semidirect |
| 37. #22576083 | C22 | semidirect |
| 41. C2×Q16×C271 | C22 | semidirect |
| 43. #103×C271 | C22 | semidirect |
| 58. Q8×D271 | D4 | semidirect |
| 141. C22×C271 | #137 | semidirect |
| 152. C2×D271 | #137 | semidirect |
| 169. C271 | #3004 | semidirect |
| 176. #451 | D271 | semidirect |
| 195. C2×Q16 | C2×D271 | semidirect |
| 211. #103 | C2×D271 | semidirect |
| 321. C22 | #22576192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D271 | 2 |
| C2×#22576192 | 2 |
| #31774410 | 2 |
| #31774052 | 2 |
| #31774051 | 2 |
| #31774038 | 2 |
| #31774037 | 2 |
| #31774036 | 2 |
| #31773904 | 2 |
| #31773859 | 2 |
| #451×C271 | 2 |
| #3004 | 271 |