Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 66 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. #91829 | C2 | semidirect |
| 2. C2×C5×#214 | C2 | semidirect |
| 3. C2×C3×#686 | C2 | semidirect |
| 4. #91368 | C2 | semidirect |
| 5. C2×#6660 | C2 | semidirect |
| 6. C2×#6653 | C2 | semidirect |
| 7. #90954 | C2 | semidirect |
| 27. C2×#686 | D3 | semidirect |
| 45. C3×#168 | D4 | semidirect |
| 46. C5×C3⋊C8 | D4 | semidirect |
| 50. C2×#214 | D5 | semidirect |
| 108. #168 | #67 | semidirect |
| 137. C3⋊C8 | C22⋊D5 | semidirect |
| 162. C3×C5 | #496 | semidirect |
| 201. C5 | #5154 | semidirect |
| 213. C3 | #65465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91829 | 2 |
| C2×C5×#214 | 2 |
| C2×C3×#686 | 2 |
| #91368 | 2 |
| C2×#6660 | 2 |
| C2×#6653 | 2 |
| #90954 | 2 |
| #65465 | 3 |
| #5154 | 5 |