Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#91234 | C2 | semidirect |
| 3. C2×C3×#4005 | C2 | semidirect |
| 4. #11746560 | C2 | semidirect |
| 5. #11746558 | C2 | semidirect |
| 27. C2×#4005 | D3 | semidirect |
| 343. C3×C5 | #2133 | semidirect |
| 397. C5 | #70128 | semidirect |
| 413. C3 | #10604999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754255 | 2 |
| C2×#91234 | 2 |
| C2×C3×#4005 | 2 |
| #11746560 | 2 |
| #11746558 | 2 |
| #10604999 | 3 |
| #70128 | 5 |