Finite Group DatabasebetaFinite Group DatabasebetaOrder 16380.
112 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C3⋊#63122 |
| commutator, hypocenter | C3×C5×C13 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C13 | C4 |
| prime radical | C32×C7×D65 | C2 |
| cosocle | C3×D65 | C2×C3×C7 |
| LCS | G ▷ C3×C5×C13 | |
| UCS | C1 ◁ C3×C7 | |
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 |
|---|---|
| C32×C7×D65 | 2 |
| C7×C3⋊#63122 | 3 |
| C3×C7×#63122 | 3 |
| C3×C7×C3⋊#261 | 5 |
| C3×C3⋊#63122 | 7 |
| C3×C7×ΓL(1,𝔽16) | 13 |