Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 94 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×#4015 | C2 | semidirect |
| 4. C3×#3940 | C2 | semidirect |
| 5. C3×C4⋊#168 | C2 | semidirect |
| 6. #65297 | C3 | direct (N × H) |
| 18. #4015 | C2×C3 | semidirect |
| 20. #3940 | C2×C3 | semidirect |
| 21. C4⋊#168 | C2×C3 | semidirect |
| 24. C3×C5×D4 | Q8 | semidirect |
| 69. C5×D4 | C3×Q8 | semidirect |
| 90. C3×D4 | Dic10 | semidirect |
| 117. C3×C5 | #476 | semidirect |
| 135. D4 | C3×Dic10 | semidirect |
| 147. C5 | C3×#476 | semidirect |
| 158. C3 | #65297 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×D4 | 2 |
| C3×#4015 | 2 |
| C3×#3964 | 2 |
| C3×#3940 | 2 |
| C3×C4⋊#168 | 2 |
| #65297 | 3 |
| C3×#476 | 5 |