Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 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. #31774617 | C2 | semidirect |
| 3. #31774302 | C2 | semidirect |
| 4. #31774233 | C2 | semidirect |
| 5. #31774222 | C2 | semidirect |
| 6. #31774183 | C2 | semidirect |
| 7. #31774178 | C2 | semidirect |
| 8. #31774143 | C2 | semidirect |
| 9. C4×#16864643 | C2 | semidirect |
| 10. #31773939 | C2 | semidirect |
| 11. #436×C271 | C2 | semidirect |
| 99. C8×C271 | #41 | semidirect |
| 122. C271 | #3353 | semidirect |
| 133. #436 | D271 | semidirect |
| 222. C8 | #16864653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774617 | 2 |
| #31774551 | 2 |
| #31774302 | 2 |
| #31774233 | 2 |
| #31774222 | 2 |
| #31774183 | 2 |
| #31774178 | 2 |
| #31774143 | 2 |
| C4×#16864643 | 2 |
| #31773939 | 2 |
| #436×C271 | 2 |
| #3353 | 271 |