Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 203 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×#6718 | C2 | direct (N × H) |
| 13. #6718 | C22 | direct (N × H) |
| 44. C22×C3×C5 | Q16 | semidirect |
| 73. C2×C3×C5 | C2×Q16 | semidirect |
| 85. C22×C5 | #216 | semidirect |
| 100. C3×C5 | C22×Q16 | semidirect |
| 101. C22×C3 | #689 | semidirect |
| 107. C2×C5 | C2×#216 | semidirect |
| 119. C2×C3 | C2×#689 | semidirect |
| 121. C5 | C22×#216 | semidirect |
| 122. C22 | #6718 | direct (N × H) |
| 128. C3 | C22×#689 | semidirect |
| 129. C2 | C2×#6718 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q8 | 2 |
| C22×Dic30 | 2 |
| C2×#6718 | 2 |
| C22×C3⋊#168 | 2 |
| C22×#689 | 3 |
| C22×#216 | 5 |