Finite Group DatabasebetaFinite Group DatabasebetaOrder 3904.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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 | C22⋊Q8×C61 | C2 |
| prime radical | C2×C22⋊D61 | C22 |
| hypercenter | C22⋊Q8 | D61 |
| hypocenter | C61 | #563 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14519776 | C2 | semidirect |
| 2. #14519775 | C2 | semidirect |
| 3. #14519772 | C2 | semidirect |
| 4. #14519772 | C2 | semidirect |
| 5. #14519770 | C2 | semidirect |
| 6. #14519770 | C2 | semidirect |
| 7. #14519768 | C2 | semidirect |
| 8. #14519767 | C2 | semidirect |
| 12. #14519756 | C2 | semidirect |
| 13. #14519755 | C2 | semidirect |
| 14. #14519753 | C2 | semidirect |
| 15. C22⋊Q8×C61 | C2 | semidirect |
| 98. C61 | #563 | semidirect |
| 113. C22⋊Q8 | D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14519776 | 2 |
| #14519775 | 2 |
| #14519772 | 2 |
| #14519770 | 2 |
| #14519768 | 2 |
| #14519767 | 2 |
| #14519763 | 2 |
| #14519760 | 2 |
| #14519759 | 2 |
| #14519756 | 2 |
| #14519755 | 2 |
| #14519753 | 2 |
| C22⋊Q8×C61 | 2 |
| #563 | 61 |