Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#22576179 | C2 | semidirect |
| 2. C2×#22576166 | C2 | semidirect |
| 3. #31774476 | C2 | semidirect |
| 4. #31774142 | C2 | semidirect |
| 5. #31774141 | C2 | semidirect |
| 6. #31774139 | C2 | semidirect |
| 7. #31774138 | C2 | semidirect |
| 8. #31774130 | C2 | semidirect |
| 9. #107×D271 | C2 | semidirect |
| 10. #31773895 | C2 | semidirect |
| 11. #466×C271 | C2 | semidirect |
| 64. C8×D271 | D4 | semidirect |
| 143. C271 | #3061 | semidirect |
| 153. #466 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576179 | 2 |
| C2×#22576166 | 2 |
| #31774476 | 2 |
| #31774142 | 2 |
| #31774141 | 2 |
| #31774139 | 2 |
| #31774138 | 2 |
| #31774130 | 2 |
| #107×D271 | 2 |
| #31773895 | 2 |
| #466×C271 | 2 |
| #3061 | 271 |