Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1734 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 264 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×C5×A4⋊Q8 | C2 | direct (N × H) |
| 9. C5×A4⋊Q8 | C22 | direct (N × H) |
| 10. C22×A4⋊Q8 | C5 | direct (N × H) |
| 18. C22×C5×A4 | Q8 | semidirect |
| 27. C2×A4⋊Q8 | C2×C5 | direct (N × H) |
| 47. C2×C5×A4 | C2×Q8 | semidirect |
| 56. A4⋊Q8 | C22×C5 | direct (N × H) |
| 60. C24×C5 | Dic6 | semidirect |
| 93. C5×A4 | C22×Q8 | semidirect |
| 96. C22×A4 | C5×Q8 | semidirect |
| 112. C23×C5 | C2×Dic6 | semidirect |
| 148. C2×A4 | C2×C5×Q8 | semidirect |
| 162. C22×C5 | A4⋊Q8 | direct (N × H) |
| 163. C22×C5 | C22×Dic6 | semidirect |
| 172. C24 | C5×Dic6 | semidirect |
| 199. A4 | C22×C5×Q8 | semidirect |
| 205. C2×C5 | C2×A4⋊Q8 | direct (N × H) |
| 216. C23 | C2×C5×Dic6 | semidirect |
| 234. C5 | C22×A4⋊Q8 | direct (N × H) |
| 244. C22 | C5×A4⋊Q8 | direct (N × H) |
| 245. C22 | C22×C5×Dic6 | semidirect |
| 255. C2 | C2×C5×A4⋊Q8 | 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 |
| C22×C5×SL(2,ℤ/4) | 2 |
| C2×C5×A4⋊Q8 | 2 |
| C22×C5×C22⋊Q8 | 3 |
| C22×C5×Dic6 | 4 |
| C22×A4⋊Q8 | 5 |