Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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×#944 | C2 | semidirect |
| 3. C2×C3×#688 | C2 | semidirect |
| 5. C2×#6660 | C2 | semidirect |
| 6. C2×#6655 | C2 | semidirect |
| 7. Dic3×#168 | C2 | semidirect |
| 27. C2×#688 | D3 | semidirect |
| 45. C3⋊#168 | D4 | semidirect |
| 46. C3×#168 | D4 | semidirect |
| 48. #944 | D5 | semidirect |
| 77. C5×Dic3 | SD16 | semidirect |
| 107. #168 | #67 | semidirect |
| 159. C3×C5 | #492 | semidirect |
| 169. Dic3 | #688 | semidirect |
| 195. C5 | #5175 | semidirect |
| 206. C3 | #65374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6717 | 2 |
| C5×#944 | 2 |
| C2×C3×#688 | 2 |
| #91458 | 2 |
| C2×#6660 | 2 |
| C2×#6655 | 2 |
| Dic3×#168 | 2 |
| #65374 | 3 |
| #5175 | 5 |