Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 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. #91793 | C2 | semidirect |
| 2. C5×#904 | C2 | semidirect |
| 3. C2×C3×#672 | C2 | semidirect |
| 4. #90948 | C2 | semidirect |
| 5. #90945 | C2 | semidirect |
| 6. #90944 | C2 | semidirect |
| 7. #90939 | C2 | semidirect |
| 27. C2×#672 | D3 | semidirect |
| 40. #904 | D5 | semidirect |
| 127. C3×C5 | #508 | semidirect |
| 154. C5 | #4904 | semidirect |
| 162. C3 | #65483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91793 | 2 |
| C5×#904 | 2 |
| C2×C3×#672 | 2 |
| #90948 | 2 |
| #90945 | 2 |
| #90944 | 2 |
| #90939 | 2 |
| #65483 | 3 |
| #4904 | 5 |