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 |
|---|---|---|
| 2. #31774471 | C2 | semidirect |
| 3. #31774380 | C2 | semidirect |
| 4. #31774121 | C2 | semidirect |
| 5. #31774114 | C2 | semidirect |
| 6. #31774105 | C2 | semidirect |
| 7. #31774100 | C2 | semidirect |
| 8. #31773925 | C2 | semidirect |
| 9. #31773899 | C2 | semidirect |
| 10. C2×#22576084 | C2 | semidirect |
| 11. C2×#137×C271 | C2 | semidirect |
| 146. C271 | #3046 | semidirect |
| 148. C2×#137 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576180 | 2 |
| #31774471 | 2 |
| #31774380 | 2 |
| #31774121 | 2 |
| #31774114 | 2 |
| #31774105 | 2 |
| #31774100 | 2 |
| #31773925 | 2 |
| #31773899 | 2 |
| C2×#22576084 | 2 |
| C2×#137×C271 | 2 |
| #3046 | 271 |