Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
688 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 688 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 |
|---|---|---|
| 2. C5×A4×Q16 | C2 | direct (N × H) |
| 4. C23×C5×Q16 | C3 | semidirect |
| 11. C2×A4×Q16 | C5 | direct (N × H) |
| 17. C22×C5×Q16 | C2×C3 | semidirect |
| 27. A4×Q16 | C2×C5 | direct (N × H) |
| 47. C2×C5×Q16 | A4 | direct (N × H) |
| 52. C23×Q16 | C3×C5 | semidirect |
| 53. C2×C5×A4 | Q16 | direct (N × H) |
| 95. C5×Q16 | C2×A4 | direct (N × H) |
| 107. C22×Q16 | C2×C3×C5 | semidirect |
| 110. C5×A4 | C2×Q16 | direct (N × H) |
| 124. C23×C5 | C3×Q16 | semidirect |
| 169. C2×Q16 | C5×A4 | direct (N × H) |
| 176. C2×A4 | C5×Q16 | direct (N × H) |
| 190. C22×C5 | C2×C3×Q16 | semidirect |
| 227. Q16 | C2×C5×A4 | direct (N × H) |
| 236. A4 | C2×C5×Q16 | direct (N × H) |
| 243. C2×C5 | A4×Q16 | direct (N × H) |
| 248. C23 | C3×C5×Q16 | semidirect |
| 277. C5 | C2×A4×Q16 | direct (N × H) |
| 285. C22 | C2×C3×C5×Q16 | semidirect |
| 297. C2 | C5×A4×Q16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×A4 | 2 |
| C5×A4×Q16 | 2 |
| C2×C5×C8×A4 | 2 |
| C23×C5×Q16 | 3 |
| C2×C3×C5×Q16 | 4 |
| C2×A4×Q16 | 5 |