Finite Group DatabasebetaFinite Group DatabasebetaOrder 27900.
212 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 48 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 | C32×C5×C31 | C22×C5 |
| LCS | G ▷ C32×C5×C31 | |
| 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 |
|---|---|
| C3⋊D15×ΓL(1,𝔽32) | 2 |
| C3×D15×ΓL(1,𝔽32) | 2 |
| C3×C5×D3×ΓL(1,𝔽32) | 2 |
| C2×D15×ΓL(1,𝔽32) | 3 |
| D3×D5×ΓL(1,𝔽32) | 3 |
| D3×D15×C31 | 5 |
| D32×ΓL(1,𝔽32) | 5 |
| C5×D3×D15 | 31 |