Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #31774378 | C2 | semidirect |
| 3. #31774008 | C2 | semidirect |
| 4. #31774003 | C2 | semidirect |
| 5. #31773984 | C2 | semidirect |
| 6. #31773896 | C2 | semidirect |
| 7. #31773852 | C2 | semidirect |
| 8. C2×#106×C271 | C2 | semidirect |
| 10. #22576182 | C4 | semidirect |
| 30. #16864654 | C2×C4 | semidirect |
| 36. Dic1084 | C2×C4 | semidirect |
| 37. #16864643 | C2×C4 | semidirect |
| 38. D2168 | C2×C4 | semidirect |
| 49. C2×C8×C271 | C2×C4 | semidirect |
| 90. C271 | #2952 | semidirect |
| 97. C2×#106 | D271 | semidirect |
| 134. C2×C8 | C4×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576182 | 2 |
| #31774378 | 2 |
| #31774008 | 2 |
| #31774003 | 2 |
| #31773984 | 2 |
| #31773896 | 2 |
| #31773852 | 2 |
| C2×#106×C271 | 2 |
| #2952 | 271 |