Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
328 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 10. #91231 | C4 | semidirect |
| 12. C3×C5×C4⋊C8 | C4 | semidirect |
| 15. C3×C4⋊#168 | C4 | semidirect |
| 44. C5×C4⋊C8 | Dic3 | semidirect |
| 47. C4⋊#168 | Dic3 | semidirect |
| 71. C3×C4⋊C8 | AGL(1,𝔽5) | semidirect |
| 145. C4⋊C8 | ΓL(1,𝔽16) | semidirect |
| 201. C3×C5 | #1285 | semidirect |
| 243. C5 | #67750 | semidirect |
| 257. C3 | #10598585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊ΓL(1,𝔽16) | 2 |
| #11752342 | 2 |
| C3×#65124 | 2 |
| #10598585 | 3 |
| #67750 | 5 |