Finite Group DatabasebetaFinite Group DatabasebetaOrder 7200.
652 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 57 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 | C22×C3×C52 | C2×C3×C4 |
| prime radical | A4×D15⋊D5 | C2 |
| cosocle | C22×C3×C5⋊D5 | C22×C3 |
| LCS | G ▷ C22×C3×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 |
|---|---|
| A4×C3⋊#1044 | 2 |
| A4×D15⋊D5 | 2 |
| C3×A4×#1043 | 2 |
| C22×#10597182 | 3 |
| A4×D5⋊AGL(1,𝔽5) | 3 |
| C3×#10597182 | 4 |
| D3×A4×AGL(1,𝔽5) | 5 |