Finite Group DatabasebetaFinite Group DatabasebetaOrder 33300.
352 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 87 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, cosocle, hypocenter | C3×C52×C37 | C22×C3 |
| LCS | G ▷ C3×C52×C37 | |
| 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 |
|---|---|
| C37⋊C3×C3⋊(C5⋊D5) | 2 |
| C3⋊(C5⋊(C5⋊(D37⋊C3))) | 2 |
| C3×C52×D37⋊C3 | 2 |
| D37×C3⋊(C5⋊D5) | 3 |
| C5⋊D5×D37⋊C3 | 3 |
| D15×D37⋊C3 | 5 |
| C2×C3×C3⋊(C5⋊D5) | 37 |