Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C2×#22576085 | C2 | semidirect |
| 4. C2×#22576083 | C2 | semidirect |
| 6. #31773659 | C2 | semidirect |
| 7. #340×C271 | C2 | semidirect |
| 15. #22576140 | C4 | semidirect |
| 131. C271 | #1894 | semidirect |
| 139. #340 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864637 | 2 |
| C2×#22576140 | 2 |
| C2×#22576085 | 2 |
| C2×#22576083 | 2 |
| #31773754 | 2 |
| #31773659 | 2 |
| #340×C271 | 2 |
| #1894 | 271 |