Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
448 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 2. #11751177 | C2 | semidirect |
| 3. #11751171 | C2 | semidirect |
| 4. #11750783 | C2 | semidirect |
| 5. C8×C3⋊#168 | C2 | semidirect |
| 58. C3×C5×C8 | SD16 | semidirect |
| 60. C3⋊#168 | D8 | semidirect |
| 116. C5×C8 | #214 | semidirect |
| 141. C3×C8 | #687 | semidirect |
| 164. C3×C5 | #1706 | semidirect |
| 188. C8 | #6716 | semidirect |
| 193. C5 | #71274 | semidirect |
| 202. C3 | #10602067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#493 | 2 |
| #11751177 | 2 |
| #11751171 | 2 |
| #11750783 | 2 |
| C8×C3⋊#168 | 2 |
| #10602067 | 3 |
| #71274 | 5 |