Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #31772623 | C2 | semidirect |
| 2. #31772621 | C2 | semidirect |
| 3. #31772618 | C2 | semidirect |
| 4. #31772614 | C2 | semidirect |
| 5. #31772612 | C2 | semidirect |
| 6. #31772609 | C2 | semidirect |
| 7. #31772605 | C2 | semidirect |
| 9. C4×Dic1082 | C2 | semidirect |
| 10. C4×C22⋊D541 | C2 | semidirect |
| 11. C4×C22⋊D541 | C2 | semidirect |
| 12. #31772587 | C2 | semidirect |
| 13. #31772585 | C2 | semidirect |
| 14. C2×C4×Dic541 | C2 | semidirect |
| 15. C4×D4×C541 | C2 | semidirect |
| 103. C541 | #529 | semidirect |
| 116. C4×D4 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772623 | 2 |
| #31772621 | 2 |
| #31772618 | 2 |
| #31772614 | 2 |
| #31772612 | 2 |
| #31772609 | 2 |
| #31772605 | 2 |
| #31772600 | 2 |
| C4×Dic1082 | 2 |
| C4×C22⋊D541 | 2 |
| #31772587 | 2 |
| #31772585 | 2 |
| C2×C4×Dic541 | 2 |
| C4×D4×C541 | 2 |
| #529 | 541 |