Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31774452 | C2 | semidirect |
| 3. #31774240 | C2 | semidirect |
| 4. #31774179 | C2 | semidirect |
| 5. #31774108 | C2 | semidirect |
| 6. #31774102 | C2 | semidirect |
| 8. #31773991 | C2 | semidirect |
| 9. #31773988 | C2 | semidirect |
| 10. #31773949 | C2 | semidirect |
| 11. #474×C271 | C2 | semidirect |
| 136. C271 | #3107 | semidirect |
| 142. #474 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774452 | 2 |
| C4×#16864653 | 2 |
| #31774240 | 2 |
| #31774179 | 2 |
| #31774108 | 2 |
| #31774102 | 2 |
| #31774060 | 2 |
| #31773991 | 2 |
| #31773988 | 2 |
| #31773949 | 2 |
| #474×C271 | 2 |
| #3107 | 271 |