Finite Group DatabasebetaFinite Group DatabasebetaOrder 32340.
400 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D3×AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C3×C11 | C22×C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C11 | C22×C5 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C72 | |
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 |
|---|---|
| D3×C72×C11⋊C5 | 2 |
| C72×C3⋊AGL(1,𝔽11) | 2 |
| C3×C72×AGL(1,𝔽11) | 2 |
| C2×C72×AGL(1,𝔽11) | 3 |
| D3×C72×D11 | 5 |
| D3×C7×AGL(1,𝔽11) | 7 |
| C2×C5×D3×C72 | 11 |