Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 84 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. #11752362 | C2 | semidirect |
| 4. C3×#64872 | C2 | semidirect |
| 5. #11746514 | C2 | semidirect |
| 7. #170⋊(C3⋊C8) | C2 | semidirect |
| 31. #64872 | D3 | semidirect |
| 83. C3×Dic10 | M16 | semidirect |
| 175. Dic10 | ΓL(1,𝔽25) | semidirect |
| 252. C3×C5 | #1588 | semidirect |
| 293. C5 | #68223 | semidirect |
| 306. C3 | #10603946 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752362 | 2 |
| #11751927 | 2 |
| #11747218 | 2 |
| C3×#64872 | 2 |
| #11746514 | 2 |
| #11746489 | 2 |
| #170⋊(C3⋊C8) | 2 |
| #10603946 | 3 |
| #68223 | 5 |