Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#22576192 | C2 | semidirect |
| 2. C2×#22576189 | C2 | semidirect |
| 4. C4⋊Q8×D271 | C2 | semidirect |
| 5. #31774292 | C2 | semidirect |
| 6. #31774291 | C2 | semidirect |
| 7. #31774289 | C2 | semidirect |
| 8. #31774275 | C2 | semidirect |
| 9. #31774268 | C2 | semidirect |
| 10. #31773849 | C2 | semidirect |
| 11. #497×C271 | C2 | semidirect |
| 63. #16864637 | D4 | semidirect |
| 124. Dic271 | #137 | semidirect |
| 130. C271 | #3152 | semidirect |
| 139. #497 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576192 | 2 |
| C2×#22576189 | 2 |
| #31774446 | 2 |
| C4⋊Q8×D271 | 2 |
| #31774292 | 2 |
| #31774291 | 2 |
| #31774289 | 2 |
| #31774275 | 2 |
| #31774268 | 2 |
| #31773849 | 2 |
| #497×C271 | 2 |
| #3152 | 271 |