Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
352 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 96 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×#65703 | C2 | semidirect |
| 4. #11746743 | C2 | semidirect |
| 5. #11746514 | C2 | semidirect |
| 7. #11746485 | C2 | semidirect |
| 25. #65703 | D3 | semidirect |
| 49. #6658 | C8 | semidirect |
| 83. C3×Dic10 | C2×C8 | semidirect |
| 92. C5×C3⋊C8 | C2×C8 | semidirect |
| 175. Dic10 | D3×C8 | semidirect |
| 221. C3⋊C8 | D5⋊C8 | semidirect |
| 252. C3×C5 | SD16⋊C8 | semidirect |
| 293. C5 | #70937 | semidirect |
| 306. C3 | #10604040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65703 | 2 |
| #11751893 | 2 |
| #11747225 | 2 |
| #11746743 | 2 |
| #11746514 | 2 |
| #11746490 | 2 |
| #11746485 | 2 |
| #10604040 | 3 |
| #70937 | 5 |