Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
356 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 112 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. C8×C3⋊#170 | C2 | semidirect |
| 5. C3×#170⋊C8 | C2 | semidirect |
| 6. #170⋊(C3⋊C8) | C2 | semidirect |
| 7. #11746485 | C2 | semidirect |
| 29. #170⋊C8 | D3 | semidirect |
| 235. C3×C5 | #1454 | semidirect |
| 274. C5 | #68074 | semidirect |
| 286. C3 | #10604014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751812 | 2 |
| #11751797 | 2 |
| #11747583 | 2 |
| C8×C3⋊#170 | 2 |
| C3×#170⋊C8 | 2 |
| #170⋊(C3⋊C8) | 2 |
| #11746485 | 2 |
| #10604014 | 3 |
| #68074 | 5 |