Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
276 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 4. #10598558 | C3 | direct (N × H) |
| 174. C3×C5 | #1291 | semidirect |
| 207. C5 | C3×#1291 | semidirect |
| 218. C3 | #10598558 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65757 | 2 |
| C3×C4×#704 | 2 |
| C3×#65008 | 2 |
| #10598558 | 3 |
| C3×#1291 | 5 |