Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
400 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 230 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 |
|---|---|---|
| 6. #65904 | C3 | direct (N × H) |
| 22. C3×C5×Q8 | Q8 | semidirect |
| 59. C5×Q8 | C3×Q8 | semidirect |
| 75. C3×Q8 | Dic10 | semidirect |
| 96. C3×C5 | #557 | semidirect |
| 107. Q8 | C3×Dic10 | semidirect |
| 116. C5 | C3×#557 | semidirect |
| 123. C3 | #65904 | 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×Q8 | 2 |
| C3×Q8×Dic5 | 2 |
| C3×#4036 | 2 |
| C3×#4015 | 2 |
| C3×C4×Dic10 | 2 |
| #65904 | 3 |
| C3×#557 | 5 |