Finite Group DatabasebetaFinite Group Databasebeta← C22×C3⋊D3×PSU(3,𝔽2) #72228458
Order 5184.
5854 conjugacy classes of subgroups; only the 856 normal subgroups are shown.
This group has 5854 conjugacy classes of subgroups — too many to draw. Only its 856 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊D3×PSU(3,𝔽2) |
| commutator, cosocle | C32×C3⋊D3 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | C2×Q8 |
| prime radical | C22×C3⋊D32 | C22 |
| hypocenter | C34 | C23×Q8 |
| LCS | G ▷ C32×C3⋊D3 ▷ C34 | |
| UCS | C1 ◁ C22 | |
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 |
|---|---|
| C22×#10620209 | 2 |
| C22×C3⋊D3×#157 | 2 |
| C22×C32×PSU(3,𝔽2) | 2 |
| C2×C3⋊D3×PSU(3,𝔽2) | 2 |
| C22×D3×PSU(3,𝔽2) | 3 |
| C22×Q8×C3⋊D3 | 9 |