Finite Group DatabasebetaFinite Group Databasebeta← C22×D3×PSU(3,𝔽2)⋊C3 #72228460
Order 5184.
1594 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 1594 conjugacy classes of subgroups — too many to draw. Only its 146 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 | D3×PSU(3,𝔽2)⋊C3 |
| commutator, cosocle, hypocenter | C3×PSU(3,𝔽2) | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33 | C2×SL(2,𝔽3) |
| LCS | G ▷ C3×PSU(3,𝔽2) | |
| 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×C3×PSU(3,𝔽2)⋊C3 | 2 |
| C2×D3×PSU(3,𝔽2)⋊C3 | 2 |
| C22×D3×PSU(3,𝔽2) | 3 |
| C23×PSU(3,𝔽2)⋊C3 | 3 |
| C22×D3×(C3⋊D3)⋊C3 | 4 |
| C22×D3×SL(2,𝔽3) | 9 |