Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11750952 | C2 | semidirect |
| 4. #11746864 | C2 | semidirect |
| 6. C3×#64699 | C2 | semidirect |
| 7. #11745859 | C2 | semidirect |
| 31. #64699 | D3 | semidirect |
| 93. C3×#168 | SD16 | semidirect |
| 187. #168 | #204 | semidirect |
| 259. C3×C5 | #1686 | semidirect |
| 301. C5 | #68592 | semidirect |
| 314. C3 | #10599205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750952 | 2 |
| #11747086 | 2 |
| #11747066 | 2 |
| #11746864 | 2 |
| C5×#4485 | 2 |
| C3×#64699 | 2 |
| #11745859 | 2 |
| #10599205 | 3 |
| #68592 | 5 |