Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774702 | C2 | semidirect |
| 2. #31774333 | C2 | semidirect |
| 3. #31774332 | C2 | semidirect |
| 4. #31774327 | C2 | semidirect |
| 5. C2×#22576101 | C2 | semidirect |
| 6. #31774314 | C2 | semidirect |
| 7. #576×C271 | C2 | semidirect |
| 10. #22576182 | C22 | semidirect |
| 11. C2×D2168 | C22 | semidirect |
| 12. #22576106 | C22 | semidirect |
| 13. #22576104 | C22 | semidirect |
| 14. #22576103 | C22 | semidirect |
| 15. #22576101 | C22 | semidirect |
| 16. #22576101 | C22 | semidirect |
| 17. #22576100 | C22 | semidirect |
| 18. C2×C271⋊C16 | C22 | semidirect |
| 21. #135×C271 | C22 | semidirect |
| 22. C2×D8×C271 | C22 | semidirect |
| 75. C271 | #3415 | semidirect |
| 78. #576 | D271 | semidirect |
| 89. #135 | C2×D271 | semidirect |
| 91. C2×D8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774702 | 2 |
| #31774333 | 2 |
| #31774332 | 2 |
| #31774327 | 2 |
| C2×#22576101 | 2 |
| #31774314 | 2 |
| #576×C271 | 2 |
| #3415 | 271 |