Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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. #31774452 | C2 | semidirect |
| 3. #31774306 | C2 | semidirect |
| 4. #31774265 | C2 | semidirect |
| 5. #31774256 | C2 | semidirect |
| 6. #31774152 | C2 | semidirect |
| 8. Q16×Dic271 | C2 | semidirect |
| 9. SD16×Dic271 | C2 | semidirect |
| 10. #31773849 | C2 | semidirect |
| 11. #497×C271 | C2 | semidirect |
| 129. C271 | #3172 | semidirect |
| 134. #497 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| #31774426 | 2 |
| #31774306 | 2 |
| #31774265 | 2 |
| #31774256 | 2 |
| #31774152 | 2 |
| #31774140 | 2 |
| Q16×Dic271 | 2 |
| SD16×Dic271 | 2 |
| #31773849 | 2 |
| #497×C271 | 2 |
| #3172 | 271 |