Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
120 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10598058 | C3 | direct (N × H) |
| 92. C3×C5 | #1369 | semidirect |
| 107. C5 | C3×#1369 | semidirect |
| 112. C3 | #10598058 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#364 | 2 |
| C3×#64683 | 2 |
| C3×#64681 | 2 |
| #10598058 | 3 |
| C3×#1369 | 5 |