Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 92 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. C3×#65876 | C2 | semidirect |
| 3. #11747064 | C2 | semidirect |
| 4. #11746910 | C2 | semidirect |
| 5. C5×D4⋊(C3⋊C8) | C2 | semidirect |
| 6. #11745855 | C2 | semidirect |
| 7. #11745841 | C2 | semidirect |
| 27. #65876 | D3 | semidirect |
| 64. D4⋊(C3⋊C8) | D5 | semidirect |
| 308. C3×C5 | #1628 | semidirect |
| 360. C5 | #71931 | semidirect |
| 377. C3 | #10598994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65876 | 2 |
| #11751116 | 2 |
| #11747064 | 2 |
| #11746910 | 2 |
| C5×D4⋊(C3⋊C8) | 2 |
| #11745855 | 2 |
| #11745841 | 2 |
| #10598994 | 3 |
| #71931 | 5 |