Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
148 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 52 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. #10598682 | C3 | direct (N × H) |
| 7. C3×C5×Q32 | C4 | semidirect |
| 9. C3×Dic40 | C4 | semidirect |
| 29. C5×Q32 | C3×C4 | semidirect |
| 31. Dic40 | C3×C4 | semidirect |
| 46. C3×Q32 | AGL(1,𝔽5) | semidirect |
| 86. Q32 | C3×AGL(1,𝔽5) | semidirect |
| 115. C3×C5 | #1416 | semidirect |
| 136. C5 | C3×#1416 | semidirect |
| 143. C3 | #10598682 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×Q32 | 2 |
| C3×#64849 | 2 |
| C3×D5⋊C32 | 2 |
| #10598682 | 3 |
| C3×#1416 | 5 |