Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 4. C22×#3992 | C3 | semidirect |
| 7. A4×#170 | C4 | semidirect |
| 8. C5×C8×A4 | C4 | semidirect |
| 10. A4×#168 | C4 | semidirect |
| 31. C22×#170 | C3×C4 | semidirect |
| 38. C22×C5×C8 | C3×C4 | semidirect |
| 39. C22×#168 | C3×C4 | semidirect |
| 48. #3992 | A4 | direct (N × H) |
| 61. C8×A4 | AGL(1,𝔽5) | semidirect |
| 101. C5×A4 | #97 | semidirect |
| 133. #170 | C4×A4 | semidirect |
| 135. C5×C8 | C4×A4 | semidirect |
| 137. #168 | C4×A4 | semidirect |
| 149. C22×C8 | C3×AGL(1,𝔽5) | semidirect |
| 169. C22×C5 | C3×#97 | semidirect |
| 214. A4 | #3992 | direct (N × H) |
| 248. C8 | A4×AGL(1,𝔽5) | semidirect |
| 251. C5 | A4×#97 | semidirect |
| 260. C22 | C3×#3992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×A4×AGL(1,𝔽5) | 2 |
| A4×D5⋊C8 | 2 |
| C8×D5×A4 | 2 |
| C22×#3992 | 3 |
| C3×#3992 | 4 |
| A4×#97 | 5 |