Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31774442 | C2 | semidirect |
| 2. #31774301 | C2 | semidirect |
| 3. #31774272 | C2 | semidirect |
| 4. #31774242 | C2 | semidirect |
| 5. #31774133 | C2 | semidirect |
| 6. #31774131 | C2 | semidirect |
| 7. D8×Dic271 | C2 | semidirect |
| 8. #31773979 | C2 | semidirect |
| 9. #31773977 | C2 | semidirect |
| 10. C2×C8×Dic271 | C2 | semidirect |
| 11. #466×C271 | C2 | semidirect |
| 82. C2×Dic271 | D8 | semidirect |
| 89. C271⋊C8 | #41 | semidirect |
| 101. C8×C271 | #41 | semidirect |
| 127. C271 | #3169 | semidirect |
| 135. #466 | D271 | semidirect |
| 229. C8 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774442 | 2 |
| #31774301 | 2 |
| #31774272 | 2 |
| #31774242 | 2 |
| #31774133 | 2 |
| #31774131 | 2 |
| D8×Dic271 | 2 |
| #31773979 | 2 |
| #31773977 | 2 |
| C2×C8×Dic271 | 2 |
| #466×C271 | 2 |
| #3169 | 271 |