Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
236 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 3. #10598688 | C3 | direct (N × H) |
| 18. C3×C42×C5 | C8 | semidirect |
| 53. C42×C5 | C3×C8 | semidirect |
| 76. C3×C42 | #170 | semidirect |
| 131. C42 | C3×#170 | semidirect |
| 132. C3×C5 | #1324 | semidirect |
| 166. C5 | C3×#1324 | semidirect |
| 177. C3 | #10598688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65225 | 2 |
| C3×#64913 | 2 |
| #10598688 | 3 |
| C3×#1324 | 5 |