Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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. #31772636 | C2 | semidirect |
| 3. #31772635 | C2 | semidirect |
| 4. #31772563 | C2 | semidirect |
| 5. #31772556 | C2 | semidirect |
| 6. C4×#16864513 | C2 | semidirect |
| 7. #104×C541 | C2 | semidirect |
| 9. #22575826 | C4 | semidirect |
| 10. #22575824 | C4 | semidirect |
| 11. #22575823 | C4 | semidirect |
| 12. #22575821 | C4 | semidirect |
| 51. C541 | #443 | semidirect |
| 58. #104 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772648 | 2 |
| #31772636 | 2 |
| #31772635 | 2 |
| #31772563 | 2 |
| #31772556 | 2 |
| C4×#16864513 | 2 |
| #104×C541 | 2 |
| #443 | 541 |