Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
166 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 2. C5×C8×A4 | C2 | semidirect |
| 3. A4×#168 | C2 | semidirect |
| 4. C22×#676 | C3 | semidirect |
| 11. C22×C5×C8 | C2×C3 | semidirect |
| 12. C22×#168 | C2×C3 | semidirect |
| 24. C8×A4 | D5 | semidirect |
| 40. #676 | A4 | direct (N × H) |
| 43. C5×A4 | M16 | semidirect |
| 65. C5×C8 | C2×A4 | semidirect |
| 67. #168 | C2×A4 | semidirect |
| 74. C22×C8 | C3×D5 | semidirect |
| 84. C22×C5 | C3×M16 | semidirect |
| 113. A4 | #676 | direct (N × H) |
| 138. C8 | D5×A4 | semidirect |
| 141. C5 | A4×M16 | semidirect |
| 150. C22 | C3×#676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×A4 | 2 |
| C5×C8×A4 | 2 |
| A4×#168 | 2 |
| C22×#676 | 3 |
| C3×#676 | 4 |
| A4×M16 | 5 |