Finite Group DatabasebetaFinite Group DatabasebetaOrder 10368.
2438 conjugacy classes of subgroups; only the 439 normal subgroups are shown.
This group has 2438 conjugacy classes of subgroups — too many to draw. Only its 439 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #72213199 |
| commutator, hypocenter | C34 | C22×C4×C8 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | C4×C8 |
| prime radical | C22×C3⋊D32 | C2×C4 |
| cosocle | #10620198 | C24 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1572 | 2 |
| C22×#13049788 | 2 |
| C2×#72213199 | 2 |
| C22×C4×AGL(1,𝔽9) | 9 |