Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
912 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 1. C2×C5×D4×A4 | C2 | semidirect |
| 2. C5×A4×D8 | C2 | direct (N × H) |
| 3. C2×C5×C8×A4 | C2 | semidirect |
| 4. C23×C5×D8 | C3 | semidirect |
| 7. C5×D4×A4 | C22 | semidirect |
| 10. C5×C8×A4 | C22 | semidirect |
| 11. C2×A4×D8 | C5 | direct (N × H) |
| 12. C23×C5×D4 | C2×C3 | semidirect |
| 17. C22×C5×D8 | C2×C3 | semidirect |
| 18. C23×C5×C8 | C2×C3 | semidirect |
| 27. C2×D4×A4 | C2×C5 | semidirect |
| 28. A4×D8 | C2×C5 | direct (N × H) |
| 29. C2×C8×A4 | C2×C5 | semidirect |
| 37. C22×C5×D4 | C22×C3 | semidirect |
| 48. C2×C5×D8 | A4 | direct (N × H) |
| 52. C22×C5×C8 | C22×C3 | semidirect |
| 53. C23×D8 | C3×C5 | semidirect |
| 56. C2×C5×A4 | D8 | direct (N × H) |
| 64. D4×A4 | C22×C5 | semidirect |
| 67. C8×A4 | C22×C5 | semidirect |
| 89. C2×C5×D4 | C2×A4 | semidirect |
| 99. C5×D8 | C2×A4 | direct (N × H) |
| 105. C2×C5×C8 | C2×A4 | semidirect |
| 106. C23×D4 | C2×C3×C5 | semidirect |
| 111. C22×D8 | C2×C3×C5 | semidirect |
| 112. C23×C8 | C2×C3×C5 | semidirect |
| 116. C5×A4 | C2×D8 | direct (N × H) |
| 144. C23×C5 | C3×D8 | semidirect |
| 153. C5×D4 | C22×A4 | semidirect |
| 164. C5×C8 | C22×A4 | semidirect |
| 172. C22×D4 | C22×C3×C5 | semidirect |
| 183. C2×D8 | C5×A4 | direct (N × H) |
| 187. C22×C8 | C22×C3×C5 | semidirect |
| 193. C2×A4 | C5×D8 | direct (N × H) |
| 216. C22×C5 | C2×C3×D8 | semidirect |
| 243. C2×D4 | C2×C5×A4 | semidirect |
| 253. D8 | C2×C5×A4 | direct (N × H) |
| 259. C2×C8 | C2×C5×A4 | semidirect |
| 264. A4 | C2×C5×D8 | direct (N × H) |
| 272. C2×C5 | A4×D8 | direct (N × H) |
| 291. C23 | C3×C5×D8 | semidirect |
| 300. D4 | C22×C5×A4 | semidirect |
| 311. C8 | C22×C5×A4 | semidirect |
| 315. C5 | C2×A4×D8 | direct (N × H) |
| 333. C22 | C2×C3×C5×D8 | semidirect |
| 345. C2 | C5×A4×D8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×A4 | 2 |
| C5×A4×D8 | 2 |
| C2×C5×C8×A4 | 2 |
| C23×C5×D8 | 3 |
| C2×C3×C5×D8 | 4 |
| C2×A4×D8 | 5 |