Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 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 |
|---|---|---|
| 4. #10598813 | C3 | direct (N × H) |
| 6. C2×C3×C5×Q16 | C4 | semidirect |
| 11. C3×#3950 | C4 | semidirect |
| 33. C2×C5×Q16 | C3×C4 | semidirect |
| 38. #3950 | C3×C4 | semidirect |
| 54. C2×C3×Q16 | AGL(1,𝔽5) | semidirect |
| 115. C2×Q16 | C3×AGL(1,𝔽5) | semidirect |
| 165. C3×C5 | #1348 | semidirect |
| 201. C5 | C3×#1348 | semidirect |
| 213. C3 | #10598813 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65477 | 2 |
| C3×#64893 | 2 |
| C3×#64887 | 2 |
| #10598813 | 3 |
| C3×#1348 | 5 |