Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
400 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 12. #91221 | C4 | semidirect |
| 13. C8×ΓL(1,𝔽16) | C4 | semidirect |
| 14. C3×C4×C5×C8 | C4 | semidirect |
| 15. C3×#3947 | C4 | semidirect |
| 16. C3×C8×Dic5 | C4 | semidirect |
| 17. C3×#3935 | C4 | semidirect |
| 54. C4×C5×C8 | Dic3 | semidirect |
| 55. #3947 | Dic3 | semidirect |
| 56. C8×Dic5 | Dic3 | semidirect |
| 57. #3935 | Dic3 | semidirect |
| 81. C3×C4×C8 | AGL(1,𝔽5) | semidirect |
| 158. C4×C8 | ΓL(1,𝔽16) | semidirect |
| 203. C3×C5 | #1747 | semidirect |
| 233. C5 | #69895 | semidirect |
| 243. C3 | #10603850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752377 | 2 |
| C3×#64978 | 2 |
| #11746768 | 2 |
| #11746766 | 2 |
| #11746734 | 2 |
| #10603850 | 3 |
| #69895 | 5 |