Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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. C22⋊C8×D271 | C2 | semidirect |
| 3. #31773744 | C2 | semidirect |
| 4. #31773635 | C2 | semidirect |
| 5. #31773633 | C2 | semidirect |
| 6. #31773631 | C2 | semidirect |
| 7. #327×C271 | C2 | semidirect |
| 8. C2×#16864653 | C4 | semidirect |
| 12. #22576140 | C4 | semidirect |
| 14. #22576131 | C4 | semidirect |
| 18. #22576118 | C4 | semidirect |
| 128. C271 | #1501 | semidirect |
| 136. #327 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774407 | 2 |
| C22⋊C8×D271 | 2 |
| #31773744 | 2 |
| #31773635 | 2 |
| #31773633 | 2 |
| #31773631 | 2 |
| #327×C271 | 2 |
| #1501 | 271 |