Finite Group DatabasebetaFinite Group DatabasebetaOrder 32340.
400 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 128 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 | D11×C5⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C5×C72×C11 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C11 | C22 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 ◁ C3 | |
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 |
|---|---|
| C3×C5×C72×D11 | 2 |
| C3×C11×C5⋊(C7⋊D7) | 2 |
| C3×C5⋊(C7⋊D77) | 2 |
| D11×C5⋊(C7⋊D7) | 3 |
| C3×D11×C7⋊D7 | 5 |
| C3×D11×D35 | 7 |
| C2×C3×C5⋊(C7⋊D7) | 11 |