Finite Group DatabasebetaFinite Group DatabasebetaOrder 27300.
104 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
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 |
|---|---|
| C3×C5×C7×D65 | 2 |
| C5×C7×#63121 | 3 |
| C7×C3⋊#63121 | 5 |
| C5×C7×C3⋊#261 | 5 |
| C5×C3⋊#63121 | 7 |
| C5×C7×ΓL(1,𝔽16) | 13 |