Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 254 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. C2×C5×Dic12 | C2 | direct (N × H) |
| 10. C5×Dic12 | C22 | direct (N × H) |
| 11. C22×Dic12 | C5 | direct (N × H) |
| 24. C2×Dic12 | C2×C5 | direct (N × H) |
| 32. C22×C3×C5 | Q16 | semidirect |
| 42. Dic12 | C22×C5 | direct (N × H) |
| 53. C2×C3×C5 | C2×Q16 | semidirect |
| 62. C22×C5 | Dic12 | direct (N × H) |
| 73. C3×C5 | C22×Q16 | semidirect |
| 74. C22×C3 | C5×Q16 | semidirect |
| 79. C2×C5 | C2×Dic12 | direct (N × H) |
| 88. C2×C3 | C2×C5×Q16 | semidirect |
| 90. C5 | C22×Dic12 | direct (N × H) |
| 91. C22 | C5×Dic12 | direct (N × H) |
| 96. C3 | C22×C5×Q16 | semidirect |
| 97. C2 | C2×C5×Dic12 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic6 | 2 |
| C22×C3×C5×C8 | 2 |
| C2×C5×Dic12 | 2 |
| C22×C5×Q16 | 3 |
| C22×Dic12 | 5 |