Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. C3×C5×#108 | C2 | semidirect |
| 4. C3×#3954 | C2 | semidirect |
| 5. C3×#3951 | C2 | semidirect |
| 6. #65182 | C3 | direct (N × H) |
| 18. C5×#108 | C2×C3 | semidirect |
| 19. #3954 | C2×C3 | semidirect |
| 20. #3951 | C2×C3 | semidirect |
| 34. C3×#108 | D5 | semidirect |
| 71. #108 | C3×D5 | semidirect |
| 98. C3×C5 | #430 | semidirect |
| 120. C5 | C3×#430 | semidirect |
| 127. C3 | #65182 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×M16 | 2 |
| C2×C3×#676 | 2 |
| C3×C5×#108 | 2 |
| C3×#3954 | 2 |
| C3×#3951 | 2 |
| #65182 | 3 |
| C3×#430 | 5 |