Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 1. #11751256 | C2 | semidirect |
| 3. C2×#91084 | C2 | semidirect |
| 4. #11750973 | C2 | semidirect |
| 5. C3×C5×#357 | C2 | semidirect |
| 6. #11746322 | C2 | semidirect |
| 7. #11746313 | C2 | semidirect |
| 27. C5×#357 | D3 | semidirect |
| 54. C3×#357 | D5 | semidirect |
| 127. #357 | D15 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | #69203 | semidirect |
| 301. C3 | #10599996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751256 | 2 |
| C2×#91110 | 2 |
| C2×#91084 | 2 |
| #11750973 | 2 |
| C3×C5×#357 | 2 |
| #11746322 | 2 |
| #11746313 | 2 |
| #10599996 | 3 |
| #69203 | 5 |