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. #31774632 | C2 | semidirect |
| 2. #31774604 | C2 | semidirect |
| 3. #31774253 | C2 | semidirect |
| 4. #31774244 | C2 | semidirect |
| 5. #31774196 | C2 | semidirect |
| 6. #31774192 | C2 | semidirect |
| 7. #31774114 | C2 | semidirect |
| 9. C8×Dic542 | C2 | semidirect |
| 10. #31773977 | C2 | semidirect |
| 11. C4×SD16×C271 | C2 | semidirect |
| 122. C271 | #3361 | semidirect |
| 133. C4×SD16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774632 | 2 |
| #31774604 | 2 |
| #31774253 | 2 |
| #31774244 | 2 |
| #31774196 | 2 |
| #31774192 | 2 |
| #31774114 | 2 |
| #31774092 | 2 |
| C8×Dic542 | 2 |
| #31773977 | 2 |
| C4×SD16×C271 | 2 |
| #3361 | 271 |