Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 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 |
|---|---|---|
| 2. #31774379 | C2 | semidirect |
| 3. #31774375 | C2 | semidirect |
| 4. #31774371 | C2 | semidirect |
| 5. C4×#16864655 | C2 | semidirect |
| 6. #117×D271 | C2 | semidirect |
| 7. #519×C271 | C2 | semidirect |
| 8. C2×#16864655 | C4 | semidirect |
| 13. Q8×Dic271 | C22 | semidirect |
| 14. C4×D1084 | C22 | semidirect |
| 15. #22576122 | C22 | semidirect |
| 17. #22576118 | C22 | semidirect |
| 18. #22576117 | C22 | semidirect |
| 20. C4⋊C4×D271 | C22 | semidirect |
| 22. C42×D271 | C22 | semidirect |
| 24. C4×Q8×C271 | C22 | semidirect |
| 27. #16864655 | C2×C4 | semidirect |
| 28. #16864655 | C2×C4 | semidirect |
| 29. C2×D1084 | C2×C4 | semidirect |
| 32. C2×C4×D271 | C2×C4 | semidirect |
| 42. C2×Q8×C271 | C2×C4 | semidirect |
| 79. C271 | #3428 | semidirect |
| 84. #519 | D271 | semidirect |
| 95. C4×Q8 | C2×D271 | semidirect |
| 109. C2×Q8 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864655 | 2 |
| #31774379 | 2 |
| #31774375 | 2 |
| #31774371 | 2 |
| C4×#16864655 | 2 |
| #117×D271 | 2 |
| #519×C271 | 2 |
| #3428 | 271 |