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. #31774516 | C2 | semidirect |
| 2. #31774295 | C2 | semidirect |
| 3. #31774256 | C2 | semidirect |
| 4. #31774152 | C2 | semidirect |
| 6. #31774123 | C2 | semidirect |
| 7. #31774009 | C2 | semidirect |
| 8. #31774004 | C2 | semidirect |
| 9. SD16×Dic271 | C2 | semidirect |
| 10. #31773851 | C2 | semidirect |
| 11. #495×C271 | C2 | semidirect |
| 109. C271 | #3173 | semidirect |
| 113. #495 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774516 | 2 |
| #31774295 | 2 |
| #31774256 | 2 |
| #31774152 | 2 |
| #31774147 | 2 |
| #31774123 | 2 |
| #31774009 | 2 |
| #31774004 | 2 |
| SD16×Dic271 | 2 |
| #31773851 | 2 |
| #495×C271 | 2 |
| #3173 | 271 |