Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
320 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 84 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. C22×C5×#106 | C3 | semidirect |
| 6. C5×C8×A4 | C4 | semidirect |
| 8. A4×#106 | C5 | direct (N × H) |
| 27. C22×C5×C8 | C3×C4 | semidirect |
| 34. C5×#106 | A4 | direct (N × H) |
| 35. C22×#106 | C3×C5 | semidirect |
| 43. C8×A4 | C4×C5 | semidirect |
| 72. C5×A4 | #106 | direct (N × H) |
| 103. C5×C8 | C4×A4 | semidirect |
| 109. C22×C8 | C3×C4×C5 | semidirect |
| 116. #106 | C5×A4 | direct (N × H) |
| 131. C22×C5 | C3×#106 | semidirect |
| 162. A4 | C5×#106 | direct (N × H) |
| 192. C8 | C4×C5×A4 | semidirect |
| 195. C5 | A4×#106 | direct (N × H) |
| 203. C22 | C3×C5×#106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C8×A4 | 2 |
| C5×A4×C4⋊C4 | 2 |
| C22×C5×#106 | 3 |
| C3×C5×#106 | 4 |
| A4×#106 | 5 |