Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
200 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 64 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×#64889 | C2 | semidirect |
| 3. C3×C8×#170 | C2 | semidirect |
| 4. #10598623 | C3 | direct (N × H) |
| 14. #64889 | C2×C3 | semidirect |
| 15. C8×#170 | C2×C3 | semidirect |
| 22. C3×Dic20 | C8 | semidirect |
| 23. C3×D40 | C8 | semidirect |
| 64. Dic20 | C3×C8 | semidirect |
| 65. D40 | C3×C8 | semidirect |
| 143. C3×C5 | #1335 | semidirect |
| 168. C5 | C3×#1335 | semidirect |
| 175. C3 | #10598623 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65184 | 2 |
| C3×#64889 | 2 |
| C3×C8×#170 | 2 |
| #10598623 | 3 |
| C3×#1335 | 5 |