Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31774454 | C2 | semidirect |
| 3. #31774239 | C2 | semidirect |
| 4. #31774193 | C2 | semidirect |
| 5. #31774188 | C2 | semidirect |
| 6. #31774108 | C2 | semidirect |
| 7. #31774103 | C2 | semidirect |
| 9. #31774005 | C2 | semidirect |
| 10. #31773999 | C2 | semidirect |
| 11. #432×C271 | C2 | semidirect |
| 136. C271 | #3116 | semidirect |
| 148. #432 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| C4×#16864654 | 2 |
| #31774239 | 2 |
| #31774193 | 2 |
| #31774188 | 2 |
| #31774108 | 2 |
| #31774103 | 2 |
| #31774061 | 2 |
| #31774005 | 2 |
| #31773999 | 2 |
| #432×C271 | 2 |
| #3116 | 271 |