Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
888 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 234 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×#66100 | C2 | semidirect |
| 2. C3×C5×#494 | C2 | semidirect |
| 3. C3×#65481 | C2 | semidirect |
| 4. C3×#65384 | C2 | semidirect |
| 5. C3×#64989 | C2 | semidirect |
| 6. #10613539 | C3 | direct (N × H) |
| 21. #66100 | C2×C3 | semidirect |
| 22. C5×#494 | C2×C3 | semidirect |
| 23. #65481 | C2×C3 | semidirect |
| 24. #65384 | C2×C3 | semidirect |
| 25. #64989 | C2×C3 | semidirect |
| 45. C3×#494 | D5 | semidirect |
| 109. #494 | C3×D5 | semidirect |
| 205. C3×C5 | #3293 | semidirect |
| 232. C5 | C3×#3293 | semidirect |
| 239. C3 | #10613539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66100 | 2 |
| C3×C5×#494 | 2 |
| C3×#65481 | 2 |
| C3×#65384 | 2 |
| C3×#64989 | 2 |
| #10613539 | 3 |
| C3×#3293 | 5 |