Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#22576095 | C2 | semidirect |
| 3. C2×#22576088 | C2 | semidirect |
| 4. #31773865 | C2 | semidirect |
| 5. #31773864 | C2 | semidirect |
| 6. C2×#22576071 | C2 | semidirect |
| 7. C2×#104×C271 | C2 | semidirect |
| 11. C2×#16864644 | C4 | semidirect |
| 12. C2×#16864642 | C4 | semidirect |
| 13. C2×#16864641 | C4 | semidirect |
| 14. C2×#16864639 | C4 | semidirect |
| 119. C271 | #1975 | semidirect |
| 124. C2×#104 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576180 | 2 |
| C2×#22576095 | 2 |
| C2×#22576088 | 2 |
| #31773865 | 2 |
| #31773864 | 2 |
| C2×#22576071 | 2 |
| C2×#104×C271 | 2 |
| #1975 | 271 |