Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#6717 | C2 | semidirect |
| 2. C5×Q8×Dic3 | C2 | semidirect |
| 3. C2×C3×#688 | C2 | semidirect |
| 5. Dic3⋊#168 | C2 | semidirect |
| 6. #90969 | C2 | semidirect |
| 7. #90964 | C2 | semidirect |
| 25. C2×#688 | D3 | semidirect |
| 33. C3×C5×Q8 | D4 | semidirect |
| 48. Q8×Dic3 | D5 | semidirect |
| 80. C5×Dic3 | SD16 | semidirect |
| 97. C5×Q8 | #67 | semidirect |
| 126. C3×Q8 | D20 | semidirect |
| 166. C3×C5 | #460 | semidirect |
| 179. Dic3 | #688 | semidirect |
| 188. Q8 | #1202 | semidirect |
| 207. C5 | #5163 | semidirect |
| 221. C3 | #65316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6717 | 2 |
| C5×Q8×Dic3 | 2 |
| C2×C3×#688 | 2 |
| #91458 | 2 |
| Dic3⋊#168 | 2 |
| #90969 | 2 |
| #90964 | 2 |
| #65316 | 3 |
| #5163 | 5 |