Finite Group DatabasebetaFinite Group DatabasebetaOrder 36540.
176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 176 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 | C3×C5×C7×C29 | C22×C3 |
| LCS | G ▷ C3×C5×C7×C29 | |
| 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)×D435 | 2 |
| C5×D3×ΓL(1,𝔽8)×C29 | 2 |
| C3×ΓL(1,𝔽8)×D145 | 2 |
| D3×C7×D145 | 3 |
| C2×ΓL(1,𝔽8)×D145 | 3 |
| D3×ΓL(1,𝔽8)×D29 | 5 |
| C3×D3×D145 | 7 |
| D3×D5×ΓL(1,𝔽8) | 29 |