Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774508 | C2 | semidirect |
| 3. #31774299 | C2 | semidirect |
| 4. #31774265 | C2 | semidirect |
| 5. #31774261 | C2 | semidirect |
| 6. #31774140 | C2 | semidirect |
| 7. #31774123 | C2 | semidirect |
| 8. #31773998 | C2 | semidirect |
| 9. SD16×Dic271 | C2 | semidirect |
| 10. #31773851 | C2 | semidirect |
| 11. #492×C271 | C2 | semidirect |
| 108. C271 | #3174 | semidirect |
| 113. #492 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774508 | 2 |
| #31774501 | 2 |
| #31774299 | 2 |
| #31774265 | 2 |
| #31774261 | 2 |
| #31774140 | 2 |
| #31774123 | 2 |
| #31773998 | 2 |
| SD16×Dic271 | 2 |
| #31773851 | 2 |
| #492×C271 | 2 |
| #3174 | 271 |