Finite Group DatabasebetaFinite Group Databasebeta← D3×C3⋊D3×AGL(1,𝔽5) #72222363
Order 2160.
776 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 112 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, hypocenter | C33×C5 | C22×C4 |
| prime radical | D3×D5×C3⋊D3 | C2 |
| cosocle | C33×D5 | C23 |
| LCS | G ▷ C33×C5 | |
| 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 |
|---|---|
| D3×D5×C3⋊D3 | 2 |
| ΓL(1,𝔽16)⋊(C3⋊D3) | 2 |
| C3⋊D3×ΓL(1,𝔽16) | 2 |
| D3×C3⋊ΓL(1,𝔽16) | 2 |
| AGL(1,𝔽5)×C3⋊(C3⋊D3) | 2 |
| C3×C3⋊D3×AGL(1,𝔽5) | 2 |
| C32×D3×AGL(1,𝔽5) | 2 |
| C2×C3⋊D3×AGL(1,𝔽5) | 3 |
| D32×AGL(1,𝔽5) | 3 |
| C4×D3×C3⋊D3 | 5 |