Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 86 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×#6710 | C2 | semidirect |
| 3. C2×#6650 | C2 | semidirect |
| 4. C3×C22⋊#168 | C2 | semidirect |
| 5. Dic3⋊#168 | C2 | semidirect |
| 6. (C2×D3)⋊#168 | C2 | semidirect |
| 7. Dic3×#168 | C2 | semidirect |
| 27. C22⋊#168 | D3 | semidirect |
| 43. C3⋊#168 | D4 | semidirect |
| 79. C5×Dic3 | M16 | semidirect |
| 163. C3×C5 | #436 | semidirect |
| 176. Dic3 | #681 | semidirect |
| 203. C5 | #4729 | semidirect |
| 217. C3 | #65301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6710 | 2 |
| C4×C5×#67 | 2 |
| C2×#6650 | 2 |
| C3×C22⋊#168 | 2 |
| Dic3⋊#168 | 2 |
| (C2×D3)⋊#168 | 2 |
| Dic3×#168 | 2 |
| #65301 | 3 |
| #4729 | 5 |