Finite Group DatabasebetaFinite Group DatabasebetaOrder 3904.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D61 |
| commutator, socle, cosocle | C22×C61 | C24 |
| Fitting | #123×C61 | C2 |
| prime radical | #14519749 | C2 |
| hypercenter | #123 | D61 |
| hypocenter | C61 | #542 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14519776 | C2 | semidirect |
| 2. #14519772 | C2 | semidirect |
| 3. #14519770 | C2 | semidirect |
| 4. #14519764 | C2 | semidirect |
| 5. #14519763 | C2 | semidirect |
| 6. #14519763 | C2 | semidirect |
| 7. #14519759 | C2 | semidirect |
| 8. #14519756 | C2 | semidirect |
| 9. #14519755 | C2 | semidirect |
| 10. #14519754 | C2 | semidirect |
| 12. #14519742 | C2 | semidirect |
| 13. C4×C22⋊D61 | C2 | semidirect |
| 14. #14519733 | C2 | semidirect |
| 15. #123×C61 | C2 | semidirect |
| 104. C61 | #542 | semidirect |
| 112. #123 | D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14519776 | 2 |
| #14519772 | 2 |
| #14519770 | 2 |
| #14519764 | 2 |
| #14519763 | 2 |
| #14519759 | 2 |
| #14519756 | 2 |
| #14519755 | 2 |
| #14519754 | 2 |
| #14519749 | 2 |
| #14519742 | 2 |
| C4×C22⋊D61 | 2 |
| #14519733 | 2 |
| #123×C61 | 2 |
| #542 | 61 |