Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
316 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 118 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.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #10599494 | C3 | direct (N × H) |
| 169. C3×C5 | #2102 | semidirect |
| 197. C5 | C3×#2102 | semidirect |
| 207. C3 | #10599494 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65414 | 2 |
| C3×#65407 | 2 |
| C3×C5×H(3,ℤ/4) | 2 |
| C3×#64753 | 2 |
| C3×#64752 | 2 |
| #10599494 | 3 |
| C3×#2102 | 5 |