Finite Group DatabasebetaFinite Group DatabasebetaOrder 32340.
168 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 47 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 | C5×C72×C11 | C22×C3 |
| LCS | G ▷ C5×C72×C11 | |
| 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 |
|---|---|
| ΓL(1,𝔽8)×D385 | 2 |
| C5⋊(C11⋊(ΓL(1,𝔽8)⋊D7)) | 2 |
| C5×C7×C11×AGL(1,𝔽7) | 2 |
| D7×D385 | 3 |
| AGL(1,𝔽7)×D77 | 5 |
| C2×C3×D385 | 7 |
| AGL(1,𝔽7)×D55 | 7 |
| AGL(1,𝔽7)×D35 | 11 |