Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
342 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 7. A4⋊#170 | C4 | semidirect |
| 8. C5×C8×A4 | C4 | semidirect |
| 10. A4×#168 | C4 | semidirect |
| 35. C22×C5×C8 | Dic3 | semidirect |
| 36. C22×#168 | Dic3 | semidirect |
| 59. C8×A4 | AGL(1,𝔽5) | semidirect |
| 100. C5×A4 | #97 | semidirect |
| 134. C5×C8 | SL(2,ℤ/4) | semidirect |
| 136. #168 | SL(2,ℤ/4) | semidirect |
| 145. C22×C8 | ΓL(1,𝔽16) | semidirect |
| 167. C22×C5 | #815 | semidirect |
| 212. A4 | #3992 | semidirect |
| 246. C8 | A4⋊AGL(1,𝔽5) | semidirect |
| 249. C5 | #73108 | semidirect |
| 258. C22 | #91221 | 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 |
| D5⋊(A4⋊C8) | 2 |
| C8×D5×A4 | 2 |
| #10604719 | 3 |
| #91221 | 4 |
| #73108 | 5 |