Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4×Dic542 | C2 | semidirect |
| 3. #31774228 | C2 | semidirect |
| 5. #31774205 | C2 | semidirect |
| 6. #31774120 | C2 | semidirect |
| 7. #31774055 | C2 | semidirect |
| 9. C4×Dic1084 | C2 | semidirect |
| 10. C4×#16864643 | C2 | semidirect |
| 11. #431×C271 | C2 | semidirect |
| 131. C271 | #3108 | semidirect |
| 143. #431 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774431 | 2 |
| C2×C4×Dic542 | 2 |
| #31774228 | 2 |
| #31774211 | 2 |
| #31774205 | 2 |
| #31774120 | 2 |
| #31774055 | 2 |
| #31774038 | 2 |
| C4×Dic1084 | 2 |
| C4×#16864643 | 2 |
| #431×C271 | 2 |
| #3108 | 271 |