Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×#4097 | C2 | semidirect |
| 3. C3×#4055 | C2 | semidirect |
| 4. C3×#4021 | C2 | semidirect |
| 5. C3×C5×#104 | C2 | semidirect |
| 6. C3×#3955 | C2 | semidirect |
| 7. C3×#3937 | C2 | semidirect |
| 8. #65114 | C3 | direct (N × H) |
| 17. C2×C3×Dic10 | C22 | semidirect |
| 18. C3×C5×M16 | C22 | semidirect |
| 19. C3×C42×C5 | C22 | semidirect |
| 23. C3×#681 | C22 | semidirect |
| 28. #4097 | C2×C3 | semidirect |
| 29. #4055 | C2×C3 | semidirect |
| 30. #4021 | C2×C3 | semidirect |
| 31. C5×#104 | C2×C3 | semidirect |
| 32. #3955 | C2×C3 | semidirect |
| 33. #3937 | C2×C3 | semidirect |
| 61. C3×#104 | D5 | semidirect |
| 71. C2×Dic10 | C22×C3 | semidirect |
| 72. C5×M16 | C22×C3 | semidirect |
| 73. C42×C5 | C22×C3 | semidirect |
| 77. #681 | C22×C3 | semidirect |
| 107. C3×M16 | C2×D5 | semidirect |
| 109. C3×C42 | C2×D5 | semidirect |
| 137. #104 | C3×D5 | semidirect |
| 192. M16 | C2×C3×D5 | semidirect |
| 194. C42 | C2×C3×D5 | semidirect |
| 195. C3×C5 | #455 | semidirect |
| 240. C5 | C3×#455 | semidirect |
| 253. C3 | #65114 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4149 | 2 |
| C3×#4097 | 2 |
| C3×#4055 | 2 |
| C3×#4021 | 2 |
| C3×C5×#104 | 2 |
| C3×#3955 | 2 |
| C3×#3937 | 2 |
| #65114 | 3 |
| C3×#455 | 5 |