Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 4. #11746754 | C2 | semidirect |
| 5. C3×#64884 | C2 | semidirect |
| 6. #11746514 | C2 | semidirect |
| 7. #11746512 | C2 | semidirect |
| 28. #64884 | D3 | semidirect |
| 49. #6651 | C8 | semidirect |
| 91. C3×#168 | C2×C8 | semidirect |
| 92. C5×C3⋊C8 | C2×C8 | semidirect |
| 182. #168 | D3×C8 | semidirect |
| 221. C3⋊C8 | D5⋊C8 | semidirect |
| 252. C3×C5 | #1565 | semidirect |
| 293. C5 | #68568 | semidirect |
| 306. C3 | #10603865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751901 | 2 |
| #11751777 | 2 |
| #11747592 | 2 |
| #11746754 | 2 |
| C3×#64884 | 2 |
| #11746514 | 2 |
| #11746512 | 2 |
| #10603865 | 3 |
| #68568 | 5 |