Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31774498 | C2 | semidirect |
| 2. #31774298 | C2 | semidirect |
| 3. #31774272 | C2 | semidirect |
| 4. #31774260 | C2 | semidirect |
| 5. #31774149 | C2 | semidirect |
| 6. #31774134 | C2 | semidirect |
| 7. #31774130 | C2 | semidirect |
| 8. #31774007 | C2 | semidirect |
| 9. C4×D2168 | C2 | semidirect |
| 10. #31773851 | C2 | semidirect |
| 11. C4×D8×C271 | C2 | semidirect |
| 123. C271 | #3176 | semidirect |
| 134. C4×D8 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774498 | 2 |
| #31774298 | 2 |
| #31774272 | 2 |
| #31774260 | 2 |
| #31774149 | 2 |
| #31774134 | 2 |
| #31774130 | 2 |
| #31774007 | 2 |
| C4×D2168 | 2 |
| #31773851 | 2 |
| C4×D8×C271 | 2 |
| #3176 | 271 |