Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11747008 | C2 | semidirect |
| 3. #11746988 | C2 | semidirect |
| 4. #11746280 | C2 | semidirect |
| 5. C5×#4459 | C2 | semidirect |
| 6. C3×#64675 | C2 | semidirect |
| 7. #11745864 | C2 | semidirect |
| 31. #64675 | D3 | semidirect |
| 56. #4459 | D5 | semidirect |
| 81. D60 | M16 | semidirect |
| 267. C3×C5 | #1586 | semidirect |
| 314. C5 | #68081 | semidirect |
| 329. C3 | #10598951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6654 | 2 |
| #11747008 | 2 |
| #11746988 | 2 |
| #11746280 | 2 |
| C5×#4459 | 2 |
| C3×#64675 | 2 |
| #11745864 | 2 |
| #10598951 | 3 |
| #68081 | 5 |