Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31774613 | C2 | semidirect |
| 2. #31774567 | C2 | semidirect |
| 3. #31774220 | C2 | semidirect |
| 4. #31774189 | C2 | semidirect |
| 5. #31774132 | C2 | semidirect |
| 6. #31774089 | C2 | semidirect |
| 7. #31774043 | C2 | semidirect |
| 8. C4×#16864643 | C2 | semidirect |
| 9. C8×D1084 | C2 | semidirect |
| 10. #31773890 | C2 | semidirect |
| 11. #486×C271 | C2 | semidirect |
| 132. C271 | #3305 | semidirect |
| 136. #486 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774613 | 2 |
| #31774567 | 2 |
| #31774220 | 2 |
| #31774189 | 2 |
| #31774132 | 2 |
| #31774089 | 2 |
| #31774043 | 2 |
| C4×#16864643 | 2 |
| C8×D1084 | 2 |
| #31773890 | 2 |
| #486×C271 | 2 |
| #3305 | 271 |