Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#22576188 | C2 | semidirect |
| 2. C2×#22576186 | C2 | semidirect |
| 3. C2×#22576156 | C2 | semidirect |
| 4. #31774365 | C2 | semidirect |
| 5. #31774096 | C2 | semidirect |
| 6. #31774091 | C2 | semidirect |
| 7. #31773920 | C2 | semidirect |
| 8. #31773901 | C2 | semidirect |
| 9. #418×C271 | C2 | semidirect |
| 15. C2×#16864643 | C22 | semidirect |
| 16. C2×#16864642 | C22 | semidirect |
| 17. C2×D2168 | C22 | semidirect |
| 18. C2×#16864639 | C22 | semidirect |
| 23. #22576125 | C22 | semidirect |
| 24. #22576122 | C22 | semidirect |
| 29. Dic271⋊C8 | C22 | semidirect |
| 30. #22576080 | C22 | semidirect |
| 34. #102×C271 | C22 | semidirect |
| 37. #16864654 | D4 | semidirect |
| 79. Dic542 | C2×D4 | semidirect |
| 84. D1084 | C2×D4 | semidirect |
| 125. Dic271 | AGL(1,ℤ/8) | semidirect |
| 132. C271 | #3038 | semidirect |
| 142. #418 | D271 | semidirect |
| 167. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576188 | 2 |
| C2×#22576186 | 2 |
| C2×#22576156 | 2 |
| #31774365 | 2 |
| #31774096 | 2 |
| #31774091 | 2 |
| #31773920 | 2 |
| #31773901 | 2 |
| #418×C271 | 2 |
| #3038 | 271 |