Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31773991 | C2 | semidirect |
| 4. #31773722 | C2 | semidirect |
| 5. #31773702 | C2 | semidirect |
| 6. #31773672 | C2 | semidirect |
| 11. #22576104 | C4 | semidirect |
| 23. Dic1084 | C2×C4 | semidirect |
| 30. C271⋊C16 | C2×C4 | semidirect |
| 67. C271 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576104 | 2 |
| #31773991 | 2 |
| D8×Dic271 | 2 |
| #31773722 | 2 |
| #31773702 | 2 |
| #31773672 | 2 |
| #357×C271 | 2 |
| #2175 | 271 |