Finite Group DatabasebetaFinite Group DatabasebetaOrder 16380.
176 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C13 | C22×C3 |
| LCS | G ▷ C3×C5×C7×C13 | |
| UCS | C1 | |
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 |
|---|---|
| C13×C3⋊(C5⋊AGL(1,𝔽7)) | 2 |
| C5×C3⋊(ΓL(1,𝔽8)⋊D13) | 2 |
| C3×ΓL(1,𝔽8)×D65 | 2 |
| D65⋊D21 | 3 |
| (C5⋊AGL(1,𝔽7))⋊D13 | 3 |
| D13×C3⋊AGL(1,𝔽7) | 5 |
| C3×D15⋊D13 | 7 |
| D5×C3⋊AGL(1,𝔽7) | 13 |