Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
912 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 195 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. C2×A4×#168 | C2 | direct (N × H) |
| 3. C24×#168 | C3 | semidirect |
| 8. A4×#168 | C22 | direct (N × H) |
| 14. C23×#168 | C2×C3 | semidirect |
| 15. C22×C5×A4 | C8 | semidirect |
| 37. C22×#168 | A4 | direct (N × H) |
| 38. C22×#168 | C22×C3 | semidirect |
| 41. C2×C5×A4 | C2×C8 | semidirect |
| 54. C24×C5 | C3×C8 | semidirect |
| 77. C2×#168 | C2×A4 | direct (N × H) |
| 85. C5×A4 | C22×C8 | semidirect |
| 88. C22×A4 | #168 | direct (N × H) |
| 103. C23×C5 | C2×C3×C8 | semidirect |
| 120. #168 | C22×A4 | direct (N × H) |
| 140. C2×A4 | C2×#168 | direct (N × H) |
| 154. C22×C5 | C8×A4 | semidirect |
| 155. C22×C5 | C22×C3×C8 | semidirect |
| 164. C24 | C3×#168 | semidirect |
| 191. A4 | C22×#168 | direct (N × H) |
| 197. C2×C5 | C2×C8×A4 | semidirect |
| 208. C23 | C2×C3×#168 | semidirect |
| 228. C5 | C22×C8×A4 | semidirect |
| 238. C22 | A4×#168 | direct (N × H) |
| 239. C22 | C22×C3×#168 | semidirect |
| 249. C2 | C2×A4×#168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×A4 | 2 |
| C2×A4×#168 | 2 |
| C24×#168 | 3 |
| C22×C3×#168 | 4 |
| C22×C8×A4 | 5 |