Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 288 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×D120 | C2 | semidirect |
| 2. C2×C5×#204 | C2 | semidirect |
| 3. #91451 | C2 | semidirect |
| 4. #91375 | C2 | semidirect |
| 5. C2×#6660 | C2 | semidirect |
| 6. C2×#6654 | C2 | semidirect |
| 7. C3×#3947 | C2 | semidirect |
| 29. #3947 | D3 | semidirect |
| 45. C3×C5×C8 | D4 | semidirect |
| 46. C3×#168 | D4 | semidirect |
| 50. C2×#204 | D5 | semidirect |
| 107. C5×C8 | D12 | semidirect |
| 108. #168 | D12 | semidirect |
| 137. C3×C8 | C22⋊D5 | semidirect |
| 162. C3×C5 | #496 | semidirect |
| 195. C8 | #1203 | semidirect |
| 201. C5 | #4712 | semidirect |
| 213. C3 | #65465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D120 | 2 |
| C2×C5×#204 | 2 |
| #91451 | 2 |
| #91375 | 2 |
| C2×#6660 | 2 |
| C2×#6654 | 2 |
| C3×#3947 | 2 |
| #65465 | 3 |
| #4712 | 5 |