Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 1. C3×#65132 | C2 | semidirect |
| 2. C3×#64984 | C2 | semidirect |
| 3. C3×#64977 | C2 | semidirect |
| 4. C3×C5×#334 | C2 | semidirect |
| 5. C3×#64705 | C2 | semidirect |
| 6. #10599333 | C3 | direct (N × H) |
| 19. #65132 | C2×C3 | semidirect |
| 20. #64984 | C2×C3 | semidirect |
| 21. #64977 | C2×C3 | semidirect |
| 22. C5×#334 | C2×C3 | semidirect |
| 23. #64705 | C2×C3 | semidirect |
| 43. C3×#334 | D5 | semidirect |
| 73. C3×C5×C8 | D8 | semidirect |
| 105. #334 | C3×D5 | semidirect |
| 151. C5×C8 | C3×D8 | semidirect |
| 186. C3×C8 | D40 | semidirect |
| 215. C3×C5 | #1687 | semidirect |
| 250. C8 | C3×D40 | semidirect |
| 256. C5 | C3×#1687 | semidirect |
| 269. C3 | #10599333 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65132 | 2 |
| C3×#64984 | 2 |
| C3×#64977 | 2 |
| C3×C5×#334 | 2 |
| C3×#64705 | 2 |
| #10599333 | 3 |
| C3×#1687 | 5 |