Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
208 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 90 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×#4053 | C2 | semidirect |
| 3. C3×C5×#108 | C2 | semidirect |
| 4. C3×#3957 | C2 | semidirect |
| 5. C3×#3947 | C2 | semidirect |
| 6. #65183 | C3 | direct (N × H) |
| 12. C3×Dic20 | C4 | semidirect |
| 13. C3×D40 | C4 | semidirect |
| 14. C3×#677 | C4 | semidirect |
| 18. #4053 | C2×C3 | semidirect |
| 20. C5×#108 | C2×C3 | semidirect |
| 21. #3957 | C2×C3 | semidirect |
| 22. #3947 | C2×C3 | semidirect |
| 35. C3×#108 | D5 | semidirect |
| 43. Dic20 | C3×C4 | semidirect |
| 44. D40 | C3×C4 | semidirect |
| 45. #677 | C3×C4 | semidirect |
| 77. #108 | C3×D5 | semidirect |
| 109. C3×C5 | #444 | semidirect |
| 132. C5 | C3×#444 | semidirect |
| 139. C3 | #65183 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4053 | 2 |
| C3×#4050 | 2 |
| C3×C5×#108 | 2 |
| C3×#3957 | 2 |
| C3×#3947 | 2 |
| #65183 | 3 |
| C3×#444 | 5 |