Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 8. C3⋊#3928 | C4 | semidirect |
| 9. C3×C5×C32 | C4 | semidirect |
| 10. C3×#3926 | C4 | semidirect |
| 28. C5×C32 | Dic3 | semidirect |
| 29. #3926 | Dic3 | semidirect |
| 40. C3×C32 | AGL(1,𝔽5) | semidirect |
| 71. C32 | ΓL(1,𝔽16) | semidirect |
| 89. C3×C5 | #1398 | semidirect |
| 103. C5 | #67600 | semidirect |
| 108. C3 | #10598488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11746715 | 2 |
| #11746713 | 2 |
| C3×#64667 | 2 |
| #10598488 | 3 |
| #67600 | 5 |