Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 54. C3×C4×C5 | Q16 | semidirect |
| 102. C4×C5 | #216 | semidirect |
| 116. C3×C5 | #462 | semidirect |
| 121. C3×C4 | #689 | semidirect |
| 142. C5 | #5031 | semidirect |
| 148. C4 | #6718 | semidirect |
| 151. C3 | #65320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| C2×#6718 | 2 |
| #91758 | 2 |
| #91094 | 2 |
| C4⋊(C3⋊#168) | 2 |
| #65320 | 3 |
| #5031 | 5 |