Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774626 | C2 | semidirect |
| 3. #31774253 | C2 | semidirect |
| 5. #31774200 | C2 | semidirect |
| 6. #31774182 | C2 | semidirect |
| 7. #31774121 | C2 | semidirect |
| 9. C8×Dic542 | C2 | semidirect |
| 10. #31773982 | C2 | semidirect |
| 11. C4×Q16×C271 | C2 | semidirect |
| 117. C271 | #3365 | semidirect |
| 128. C4×Q16 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774632 | 2 |
| #31774626 | 2 |
| #31774253 | 2 |
| #31774244 | 2 |
| #31774200 | 2 |
| #31774182 | 2 |
| #31774121 | 2 |
| #31774097 | 2 |
| C8×Dic542 | 2 |
| #31773982 | 2 |
| C4×Q16×C271 | 2 |
| #3365 | 271 |