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×#22576191 | C2 | semidirect |
| 3. #31774377 | C2 | semidirect |
| 4. #31774116 | C2 | semidirect |
| 5. #31774109 | C2 | semidirect |
| 6. #31774104 | C2 | semidirect |
| 7. #31774099 | C2 | semidirect |
| 8. #31773924 | C2 | semidirect |
| 9. #31773898 | C2 | semidirect |
| 10. C2×#22576084 | C2 | semidirect |
| 11. #536×C271 | C2 | semidirect |
| 146. C271 | #3046 | semidirect |
| 150. #536 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576191 | 2 |
| C2×#22576180 | 2 |
| #31774377 | 2 |
| #31774116 | 2 |
| #31774109 | 2 |
| #31774104 | 2 |
| #31774099 | 2 |
| #31773924 | 2 |
| #31773898 | 2 |
| C2×#22576084 | 2 |
| #536×C271 | 2 |
| #3046 | 271 |