Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31774627 | C2 | semidirect |
| 3. #31774242 | C2 | semidirect |
| 4. #31774185 | C2 | semidirect |
| 5. #31774184 | C2 | semidirect |
| 6. #31774096 | C2 | semidirect |
| 7. #31774094 | C2 | semidirect |
| 8. C8×Dic542 | C2 | semidirect |
| 9. #31773988 | C2 | semidirect |
| 10. C4×#16864643 | C2 | semidirect |
| 11. #486×C271 | C2 | semidirect |
| 77. Dic542 | SD16 | semidirect |
| 78. Dic542 | #41 | semidirect |
| 125. C271 | #3362 | semidirect |
| 130. #486 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774627 | 2 |
| #31774567 | 2 |
| #31774242 | 2 |
| #31774185 | 2 |
| #31774184 | 2 |
| #31774096 | 2 |
| #31774094 | 2 |
| C8×Dic542 | 2 |
| #31773988 | 2 |
| C4×#16864643 | 2 |
| #486×C271 | 2 |
| #3362 | 271 |