Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31774733 | C2 | semidirect |
| 2. C2×#22576188 | C2 | semidirect |
| 3. #31774461 | C2 | semidirect |
| 4. #31774072 | C2 | semidirect |
| 5. #31774067 | C2 | semidirect |
| 6. #31773913 | C2 | semidirect |
| 7. #413×C271 | C2 | semidirect |
| 8. #22576208 | C22 | semidirect |
| 12. #22576205 | C22 | semidirect |
| 16. C22×D1084 | C22 | semidirect |
| 18. #22576188 | C22 | semidirect |
| 21. #22576156 | C22 | semidirect |
| 22. #22576149 | C22 | semidirect |
| 25. #22576119 | C22 | semidirect |
| 26. #22576086 | C22 | semidirect |
| 28. C2×M16×C271 | C22 | semidirect |
| 29. #101×C271 | C22 | semidirect |
| 30. #100×C271 | C22 | semidirect |
| 38. #16864654 | D4 | semidirect |
| 43. C2×Dic542 | D4 | semidirect |
| 49. C2×D1084 | D4 | semidirect |
| 134. C271 | #3021 | semidirect |
| 142. #413 | D271 | semidirect |
| 157. C2×M16 | C2×D271 | semidirect |
| 164. #101 | C2×D271 | semidirect |
| 165. #100 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774733 | 2 |
| C2×#22576188 | 2 |
| #31774461 | 2 |
| #31774072 | 2 |
| #31774067 | 2 |
| #31773913 | 2 |
| #413×C271 | 2 |
| #3021 | 271 |