Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
252 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 252 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×#64893 | C2 | semidirect |
| 3. C3×#64887 | C2 | semidirect |
| 4. #10598805 | C3 | direct (N × H) |
| 6. C2×C3×C5×D8 | C4 | semidirect |
| 11. C3×#3950 | C4 | semidirect |
| 14. #64893 | C2×C3 | semidirect |
| 15. #64887 | C2×C3 | semidirect |
| 33. C2×C5×D8 | C3×C4 | semidirect |
| 38. #3950 | C3×C4 | semidirect |
| 56. C2×C3×D8 | AGL(1,𝔽5) | semidirect |
| 121. C2×D8 | C3×AGL(1,𝔽5) | semidirect |
| 176. C3×C5 | #1347 | semidirect |
| 218. C5 | C3×#1347 | semidirect |
| 232. C3 | #10598805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65446 | 2 |
| C3×#64893 | 2 |
| C3×#64887 | 2 |
| #10598805 | 3 |
| C3×#1347 | 5 |