Finite Group DatabasebetaFinite Group DatabasebetaOrder 36544.
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. #32912702 | C2 | semidirect |
| 3. #32912701 | C2 | semidirect |
| 4. #32912629 | C2 | semidirect |
| 5. #32912622 | C2 | semidirect |
| 6. C4×C571⋊C8 | C2 | semidirect |
| 7. #104×C571 | C2 | semidirect |
| 9. #22603723 | C4 | semidirect |
| 10. #22603721 | C4 | semidirect |
| 11. #22603720 | C4 | semidirect |
| 12. #22603718 | C4 | semidirect |
| 51. C571 | #443 | semidirect |
| 58. #104 | D571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #32912714 | 2 |
| #32912702 | 2 |
| #32912701 | 2 |
| #32912629 | 2 |
| #32912622 | 2 |
| C4×C571⋊C8 | 2 |
| #104×C571 | 2 |
| #443 | 571 |