Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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×#22576193 | C2 | semidirect |
| 3. #31774473 | C2 | semidirect |
| 4. #31774377 | C2 | semidirect |
| 5. #31774120 | C2 | semidirect |
| 6. #31774113 | C2 | semidirect |
| 7. #31774108 | C2 | semidirect |
| 8. #31774103 | C2 | semidirect |
| 9. #31773899 | C2 | semidirect |
| 10. C2×#22576085 | C2 | semidirect |
| 11. #424×C271 | C2 | semidirect |
| 146. C271 | #3046 | semidirect |
| 156. #424 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576193 | 2 |
| C2×#22576182 | 2 |
| #31774473 | 2 |
| #31774377 | 2 |
| #31774120 | 2 |
| #31774113 | 2 |
| #31774108 | 2 |
| #31774103 | 2 |
| #31773899 | 2 |
| C2×#22576085 | 2 |
| #424×C271 | 2 |
| #3046 | 271 |