Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×#709 | C2 | semidirect |
| 2. C3×C5×#121 | C2 | semidirect |
| 3. C2×C3×#687 | C2 | semidirect |
| 4. C2×C3×#686 | C2 | semidirect |
| 5. C3×C22⋊#168 | C2 | semidirect |
| 6. C3×#3942 | C2 | semidirect |
| 7. C3×#3941 | C2 | semidirect |
| 8. #65326 | C3 | direct (N × H) |
| 25. C2×#709 | C2×C3 | semidirect |
| 26. C5×#121 | C2×C3 | semidirect |
| 27. C2×#687 | C2×C3 | semidirect |
| 28. C2×#686 | C2×C3 | semidirect |
| 29. C22⋊#168 | C2×C3 | semidirect |
| 30. #3942 | C2×C3 | semidirect |
| 31. #3941 | C2×C3 | semidirect |
| 46. C3×D20 | D4 | semidirect |
| 49. C3×Dic10 | D4 | semidirect |
| 55. C3×#121 | D5 | semidirect |
| 119. D20 | C3×D4 | semidirect |
| 122. Dic10 | C3×D4 | semidirect |
| 128. #121 | C3×D5 | semidirect |
| 188. C3×C5 | #449 | semidirect |
| 236. C5 | C3×#449 | semidirect |
| 252. C3 | #65326 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#709 | 2 |
| C3×C5×#121 | 2 |
| C2×C3×#687 | 2 |
| C2×C3×#686 | 2 |
| C3×C22⋊#168 | 2 |
| C3×#3942 | 2 |
| C3×#3941 | 2 |
| #65326 | 3 |
| C3×#449 | 5 |