Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #31774431 | C2 | semidirect |
| 2. #31774303 | C2 | semidirect |
| 3. #31774284 | C2 | semidirect |
| 4. #31774261 | C2 | semidirect |
| 5. #31774259 | C2 | semidirect |
| 6. #31774148 | C2 | semidirect |
| 7. #31774141 | C2 | semidirect |
| 8. C4×#16864642 | C2 | semidirect |
| 9. C4×#16864639 | C2 | semidirect |
| 10. C4×#16864638 | C2 | semidirect |
| 11. #532×C271 | C2 | semidirect |
| 91. C271⋊C8 | #41 | semidirect |
| 137. C271 | #3171 | semidirect |
| 139. #532 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774431 | 2 |
| #31774303 | 2 |
| #31774284 | 2 |
| #31774261 | 2 |
| #31774259 | 2 |
| #31774148 | 2 |
| #31774141 | 2 |
| C4×#16864642 | 2 |
| C4×#16864639 | 2 |
| C4×#16864638 | 2 |
| #532×C271 | 2 |
| #3171 | 271 |