Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×C3×C5×Q32 | C2 | semidirect |
| 4. C2×C3×#3961 | C2 | semidirect |
| 5. C3×#64784 | C2 | semidirect |
| 7. C3×#64723 | C2 | semidirect |
| 8. #10602295 | C3 | direct (N × H) |
| 26. C2×C5×Q32 | C2×C3 | semidirect |
| 28. C2×#3961 | C2×C3 | semidirect |
| 29. #64784 | C2×C3 | semidirect |
| 31. #64723 | C2×C3 | semidirect |
| 58. C2×C3×Q32 | D5 | semidirect |
| 140. C2×Q32 | C3×D5 | semidirect |
| 148. C2×C3×D5 | Q32 | semidirect |
| 242. C2×D5 | C3×Q32 | semidirect |
| 274. C3×C5 | #2188 | semidirect |
| 314. C5 | C3×#2188 | semidirect |
| 326. C3 | #10602295 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D5×Q16 | 2 |
| C2×C3×C5×Q32 | 2 |
| C3×#65477 | 2 |
| C2×C3×#3961 | 2 |
| C3×#64784 | 2 |
| C3×#64727 | 2 |
| C3×#64723 | 2 |
| #10602295 | 3 |
| C3×#2188 | 5 |