Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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. #31774374 | C2 | semidirect |
| 3. #31773871 | C2 | semidirect |
| 4. #31773870 | C2 | semidirect |
| 5. #31773869 | C2 | semidirect |
| 6. #410×C271 | C2 | semidirect |
| 9. C2×#16864654 | C4 | semidirect |
| 11. C2×#16864653 | C4 | semidirect |
| 13. C22×Dic542 | C4 | semidirect |
| 15. C2×Q8×D271 | C4 | semidirect |
| 113. C271 | #2884 | semidirect |
| 120. #410 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576207 | 2 |
| #31774374 | 2 |
| #31773871 | 2 |
| #31773870 | 2 |
| #31773869 | 2 |
| #410×C271 | 2 |
| #2884 | 271 |