Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 108 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×#65761 | C2 | semidirect |
| 3. C3×#65745 | C2 | semidirect |
| 4. C3×#64864 | C2 | semidirect |
| 5. #10604382 | C3 | direct (N × H) |
| 7. C22×C3×D20 | C4 | semidirect |
| 10. C3×C5×#117 | C4 | semidirect |
| 13. C3×#4028 | C4 | semidirect |
| 23. #65761 | C2×C3 | semidirect |
| 24. #65745 | C2×C3 | semidirect |
| 25. #64864 | C2×C3 | semidirect |
| 58. C22×D20 | C3×C4 | semidirect |
| 61. C5×#117 | C3×C4 | semidirect |
| 64. #4028 | C3×C4 | semidirect |
| 111. C3×#117 | AGL(1,𝔽5) | semidirect |
| 230. #117 | C3×AGL(1,𝔽5) | semidirect |
| 314. C3×C5 | #2122 | semidirect |
| 373. C5 | C3×#2122 | semidirect |
| 392. C3 | #10604382 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65859 | 2 |
| C3×#65761 | 2 |
| C3×#65745 | 2 |
| C3×#64864 | 2 |
| #10604382 | 3 |
| C3×#2122 | 5 |