Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 216 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×C5×C4⋊Q8 | C2 | semidirect |
| 4. C3×#3939 | C2 | semidirect |
| 5. C3×C4⋊#168 | C2 | semidirect |
| 6. #65376 | C3 | direct (N × H) |
| 17. C5×C4⋊Q8 | C2×C3 | semidirect |
| 20. #3939 | C2×C3 | semidirect |
| 21. C4⋊#168 | C2×C3 | semidirect |
| 30. C3×D20 | Q8 | semidirect |
| 33. C3×C4⋊Q8 | D5 | semidirect |
| 75. D20 | C3×Q8 | semidirect |
| 78. C4⋊Q8 | C3×D5 | semidirect |
| 117. C3×C5 | #474 | semidirect |
| 147. C5 | C3×#474 | semidirect |
| 158. C3 | #65376 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C3×C4×D20 | 2 |
| C3×#3941 | 2 |
| C3×#3939 | 2 |
| C3×C4⋊#168 | 2 |
| #65376 | 3 |
| C3×#474 | 5 |