Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 128 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×C4×#700 | C2 | semidirect |
| 3. C3×#64921 | C2 | semidirect |
| 4. #10604597 | C3 | direct (N × H) |
| 17. C4×#700 | C2×C3 | semidirect |
| 18. #64921 | C2×C3 | semidirect |
| 185. C3×C5 | #1525 | semidirect |
| 219. C5 | C3×#1525 | semidirect |
| 230. C3 | #10604597 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66050 | 2 |
| C3×C4×#700 | 2 |
| C3×#64921 | 2 |
| #10604597 | 3 |
| C3×#1525 | 5 |