Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 6. #10601709 | C3 | direct (N × H) |
| 103. C3×C4×C5 | Q32 | semidirect |
| 166. C4×C5 | C3×Q32 | semidirect |
| 186. C3×C5 | #2209 | semidirect |
| 192. C3×C4 | #3961 | semidirect |
| 214. C5 | C3×#2209 | semidirect |
| 220. C4 | C3×#3961 | semidirect |
| 223. C3 | #10601709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q16 | 2 |
| C2×C3×#3961 | 2 |
| C3×#64988 | 2 |
| C3×#64712 | 2 |
| C3×C4⋊#672 | 2 |
| #10601709 | 3 |
| C3×#2209 | 5 |