Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
752 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 64 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. C24×C5×C8 | C3 | semidirect |
| 5. C8×C22⋊A4 | C5 | direct (N × H) |
| 9. C5×C22⋊A4 | C8 | direct (N × H) |
| 18. C22×C5×C8 | A4 | semidirect |
| 19. C24×C8 | C3×C5 | semidirect |
| 26. C24×C5 | C3×C8 | semidirect |
| 39. C22⋊A4 | C5×C8 | direct (N × H) |
| 50. C5×C8 | C22⋊A4 | direct (N × H) |
| 57. C22×C8 | C5×A4 | semidirect |
| 65. C22×C5 | C8×A4 | semidirect |
| 70. C24 | C3×C5×C8 | semidirect |
| 93. C8 | C5×C22⋊A4 | direct (N × H) |
| 95. C5 | C8×C22⋊A4 | direct (N × H) |
| 100. C22 | C5×C8×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×C22⋊A4 | 2 |
| C24×C5×C8 | 3 |
| C5×C8×A4 | 4 |
| C8×C22⋊A4 | 5 |