Finite Group DatabasebetaFinite Group Databasebeta← C22×C3×C5×AGL(2,𝔽3) #72219450
Order 25920.
2706 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 2706 conjugacy classes of subgroups — too many to draw. Only its 168 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×C5 | AGL(2,𝔽3) |
| commutator, cosocle, hypocenter | PSU(3,𝔽2)⋊C3 | C23×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33×C5 | GL(2,𝔽3) |
| LCS | G ▷ PSU(3,𝔽2)⋊C3 | |
| UCS | C1 ◁ C22×C3×C5 | |
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×C5×GL(2,𝔽3) | 9 |
| C22×C3×C5×((C3⋊D3)⋊C3)⋊C2 | 4 |
| C22×C3×C5×AΓL(1,𝔽9) | 3 |
| C22×C5×AGL(2,𝔽3) | 3 |
| C22×C3×C5×PSU(3,𝔽2)⋊C3 | 2 |
| C22×C3×AGL(2,𝔽3) | 5 |
| C2×C3×C5×AGL(2,𝔽3) | 2 |