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×#22576183 | C2 | semidirect |
| 2. C2×#22576166 | C2 | semidirect |
| 3. #31774477 | C2 | semidirect |
| 4. #31774146 | C2 | semidirect |
| 5. #31774145 | C2 | semidirect |
| 6. #31774135 | C2 | semidirect |
| 7. #31774134 | C2 | semidirect |
| 8. #31774133 | C2 | semidirect |
| 9. #107×D271 | C2 | semidirect |
| 10. #31773897 | C2 | semidirect |
| 11. #467×C271 | C2 | semidirect |
| 65. C8×D271 | D4 | semidirect |
| 143. C271 | #3061 | semidirect |
| 151. #467 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576183 | 2 |
| C2×#22576166 | 2 |
| #31774477 | 2 |
| #31774146 | 2 |
| #31774145 | 2 |
| #31774135 | 2 |
| #31774134 | 2 |
| #31774133 | 2 |
| #107×D271 | 2 |
| #31773897 | 2 |
| #467×C271 | 2 |
| #3061 | 271 |