Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
146 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 3. C22×C5×Q16 | C3 | semidirect |
| 7. A4×Q16 | C5 | direct (N × H) |
| 26. C5×Q16 | A4 | direct (N × H) |
| 29. C22×Q16 | C3×C5 | semidirect |
| 30. C5×A4 | Q16 | direct (N × H) |
| 58. C22×C5 | C3×Q16 | semidirect |
| 71. Q16 | C5×A4 | direct (N × H) |
| 75. A4 | C5×Q16 | direct (N × H) |
| 93. C5 | A4×Q16 | direct (N × H) |
| 96. C22 | C3×C5×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×A4 | 2 |
| C5×C8×A4 | 2 |
| C22×C5×Q16 | 3 |
| C3×C5×Q16 | 4 |
| A4×Q16 | 5 |