Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
220 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 3. #10598517 | C3 | direct (N × H) |
| 6. C3×#4015 | C4 | semidirect |
| 8. C3×C4×C5×C8 | C4 | semidirect |
| 24. #4015 | C3×C4 | semidirect |
| 26. C4×C5×C8 | C3×C4 | semidirect |
| 41. C3×C4×C8 | AGL(1,𝔽5) | semidirect |
| 80. C4×C8 | C3×AGL(1,𝔽5) | semidirect |
| 108. C3×C5 | #1409 | semidirect |
| 131. C5 | C3×#1409 | semidirect |
| 139. C3 | #10598517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64982 | 2 |
| C3×#64853 | 2 |
| #10598517 | 3 |
| C3×#1409 | 5 |