Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
268 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C3⋊#168 | C2 | semidirect |
| 3. #91114 | C2 | semidirect |
| 4. C4⋊(C3⋊#168) | C2 | semidirect |
| 5. C4×C3⋊#168 | C2 | semidirect |
| 23. C3×C5×D4 | C8 | semidirect |
| 32. C3⋊#168 | D4 | direct (N × H) |
| 50. C22×C3×C5 | C2×C8 | semidirect |
| 54. C3×C4×C5 | C2×C8 | semidirect |
| 67. C5×D4 | C3⋊C8 | semidirect |
| 87. C3×D4 | #168 | semidirect |
| 99. C22×C5 | C2×C3⋊C8 | semidirect |
| 103. C4×C5 | C2×C3⋊C8 | semidirect |
| 115. C3×C5 | C8×D4 | semidirect |
| 118. C22×C3 | C2×#168 | semidirect |
| 122. C3×C4 | C2×#168 | semidirect |
| 130. D4 | C3⋊#168 | direct (N × H) |
| 144. C5 | D4×C3⋊C8 | semidirect |
| 147. C22 | C2×C3⋊#168 | semidirect |
| 151. C4 | C2×C3⋊#168 | semidirect |
| 154. C3 | D4×#168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×D4 | 2 |
| C22×C3⋊#168 | 2 |
| #91114 | 2 |
| C4⋊(C3⋊#168) | 2 |
| C4×C3⋊#168 | 2 |
| D4×#168 | 3 |
| D4×C3⋊C8 | 5 |