Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3959 | C2 | semidirect |
| 3. C2×C3×#3932 | C2 | semidirect |
| 4. C3×#65162 | C2 | semidirect |
| 5. C3×C5×#357 | C2 | semidirect |
| 6. C3×#64721 | C2 | semidirect |
| 7. C3×#64711 | C2 | semidirect |
| 8. #10599997 | C3 | direct (N × H) |
| 24. C2×#3959 | C2×C3 | semidirect |
| 25. C2×#3932 | C2×C3 | semidirect |
| 26. #65162 | C2×C3 | semidirect |
| 27. C5×#357 | C2×C3 | semidirect |
| 28. #64721 | C2×C3 | semidirect |
| 29. #64711 | C2×C3 | semidirect |
| 45. C3×Dic20 | D4 | semidirect |
| 56. C3×#357 | D5 | semidirect |
| 117. Dic20 | C3×D4 | semidirect |
| 128. #357 | C3×D5 | semidirect |
| 141. C3×Dic5 | SD32 | semidirect |
| 228. Dic5 | C3×SD32 | semidirect |
| 249. C3×C5 | #2207 | semidirect |
| 291. C5 | C3×#2207 | semidirect |
| 305. C3 | #10599997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65440 | 2 |
| C2×C3×#3959 | 2 |
| C2×C3×#3932 | 2 |
| C3×#65162 | 2 |
| C3×C5×#357 | 2 |
| C3×#64721 | 2 |
| C3×#64711 | 2 |
| #10599997 | 3 |
| C3×#2207 | 5 |