Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
376 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 376 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×#65123 | C2 | semidirect |
| 2. #11747066 | C2 | semidirect |
| 4. #11746889 | C2 | semidirect |
| 5. #11746303 | C2 | semidirect |
| 6. C5×#4485 | C2 | semidirect |
| 7. #11745864 | C2 | semidirect |
| 28. #65123 | D3 | semidirect |
| 56. #4485 | D5 | semidirect |
| 90. C3×D20 | SD16 | semidirect |
| 96. C3×#168 | D8 | semidirect |
| 187. D20 | #204 | semidirect |
| 196. #168 | #213 | semidirect |
| 274. C3×C5 | #1665 | semidirect |
| 322. C5 | #70846 | semidirect |
| 337. C3 | #10599187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65123 | 2 |
| #11747066 | 2 |
| #11747026 | 2 |
| #11746889 | 2 |
| #11746303 | 2 |
| C5×#4485 | 2 |
| #11745864 | 2 |
| #10599187 | 3 |
| #70846 | 5 |