Finite Group DatabasebetaFinite Group Databasebeta← AGL(1,𝔽5)×ΓL(1,𝔽16)⋊D3 #72231146
Order 7200.
1009 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1009 conjugacy classes of subgroups — too many to draw. Only its 130 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 | C32×C52 | C2×C42 |
| prime radical | D52×C3⋊D3 | C22 |
| cosocle | C32×D52 | C23 |
| LCS | G ▷ C32×C52 | |
| 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 |
|---|---|
| #72231118 | 2 |
| C3×AGL(1,𝔽5)×ΓL(1,𝔽16) | 2 |
| D5×C3⋊D3×AGL(1,𝔽5) | 2 |
| D5×ΓL(1,𝔽16)⋊D3 | 2 |
| D3×AGL(1,𝔽5)2 | 3 |
| #72222582 | 2 |
| C4×ΓL(1,𝔽16)⋊D3 | 5 |
| AGL(1,𝔽5)×#624 | 5 |