Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
480 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 100 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. #11746369 | C2 | semidirect |
| 4. C3×#64768 | C2 | semidirect |
| 5. #11746016 | C2 | semidirect |
| 25. #64768 | D3 | direct (N × H) |
| 214. C5×D3 | #356 | semidirect |
| 276. C3×C5 | C2×#356 | semidirect |
| 320. D3 | #64768 | direct (N × H) |
| 321. C5 | D3×#356 | semidirect |
| 334. C3 | C2×#64768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×C4⋊Q8 | 2 |
| D3×#3968 | 2 |
| #11746369 | 2 |
| C3×#64768 | 2 |
| #11746016 | 2 |
| C2×#64768 | 3 |
| D3×#356 | 5 |