Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22576192 | C2 | semidirect |
| 2. #31774562 | C2 | semidirect |
| 4. #31774152 | C2 | semidirect |
| 5. #31774104 | C2 | semidirect |
| 6. #31774099 | C2 | semidirect |
| 7. #31774058 | C2 | semidirect |
| 8. #31774051 | C2 | semidirect |
| 9. C4×#16864643 | C2 | semidirect |
| 10. #31773976 | C2 | semidirect |
| 11. #494×C271 | C2 | semidirect |
| 56. #16864643 | D4 | semidirect |
| 122. C4×C271 | #137 | semidirect |
| 134. C271 | #3276 | semidirect |
| 139. #494 | D271 | semidirect |
| 261. C4 | #22576192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576192 | 2 |
| #31774562 | 2 |
| #31774550 | 2 |
| #31774152 | 2 |
| #31774104 | 2 |
| #31774099 | 2 |
| #31774058 | 2 |
| #31774051 | 2 |
| C4×#16864643 | 2 |
| #31773976 | 2 |
| #494×C271 | 2 |
| #3276 | 271 |