Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 1. C3×C4×C5×Q8 | C2 | semidirect |
| 2. C2×#6717 | C2 | semidirect |
| 4. #91093 | C2 | semidirect |
| 5. C4⋊(C3⋊#168) | C2 | semidirect |
| 18. C4×C5×Q8 | D3 | semidirect |
| 25. C3×C5×Q8 | D4 | semidirect |
| 36. C3×C4×Q8 | D5 | semidirect |
| 59. C3×C4×C5 | SD16 | semidirect |
| 74. C5×Q8 | D12 | semidirect |
| 87. C4×Q8 | D15 | semidirect |
| 96. C3×Q8 | D20 | semidirect |
| 114. C4×C5 | #215 | semidirect |
| 127. C3×C5 | #460 | semidirect |
| 135. C3×C4 | #688 | semidirect |
| 144. Q8 | D60 | semidirect |
| 159. C5 | #5027 | semidirect |
| 167. C4 | #6717 | semidirect |
| 170. C3 | #65316 | 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×#6717 | 2 |
| #91763 | 2 |
| #91093 | 2 |
| C4⋊(C3⋊#168) | 2 |
| #65316 | 3 |
| #5027 | 5 |