Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 103. C3×C4×C5 | Q32 | semidirect |
| 166. C4×C5 | #829 | semidirect |
| 186. C3×C5 | #2209 | semidirect |
| 191. C3×C4 | #3961 | semidirect |
| 214. C5 | #70916 | semidirect |
| 220. C4 | #91113 | semidirect |
| 223. C3 | #10601709 | semidirect |
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×#91113 | 2 |
| #11750800 | 2 |
| #11746313 | 2 |
| C4⋊(C3⋊#672) | 2 |
| #10601709 | 3 |
| #70916 | 5 |