Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
144 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 2. C3×#64726 | C2 | semidirect |
| 3. C2×C3×#3926 | C2 | semidirect |
| 4. #10598320 | C3 | direct (N × H) |
| 14. #64726 | C2×C3 | semidirect |
| 15. C2×#3926 | C2×C3 | semidirect |
| 113. C3×C5 | #1417 | semidirect |
| 133. C5 | C3×#1417 | semidirect |
| 139. C3 | #10598320 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#508 | 2 |
| C3×#64726 | 2 |
| C2×C3×#3926 | 2 |
| #10598320 | 3 |
| C3×#1417 | 5 |