Finite Group DatabasebetaFinite Group DatabasebetaOrder 14400.
1674 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1674 conjugacy classes of subgroups — too many to draw. Only its 195 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 | C2 | #72224613 |
| commutator, hypocenter | C32×C52 | C2×C4×C8 |
| Fitting, socle | C2×C32×C52 | C2×C42 |
| prime radical | C2×C3⋊D3×C5⋊D5 | C2×C4 |
| cosocle | C32×#6036 | C23 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C2 | |
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 |
|---|---|
| #72231171 | 2 |
| #72231170 | 2 |
| C3×#72229763 | 2 |
| C3⋊D3×#87830 | 2 |
| D3×#11717300 | 3 |
| AGL(1,𝔽5)×#3710 | 5 |