Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 108 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. #11750931 | C2 | semidirect |
| 5. C3×#64700 | C2 | semidirect |
| 6. #11745844 | C2 | semidirect |
| 7. C3⋊C8×#168 | C2 | semidirect |
| 29. #64700 | D3 | semidirect |
| 48. #6659 | C8 | semidirect |
| 80. Dic30 | C2×C8 | semidirect |
| 88. C3⋊#168 | SD16 | semidirect |
| 91. C3×#168 | C2×C8 | semidirect |
| 182. #168 | D3×C8 | semidirect |
| 252. C3×C5 | C8×SD16 | semidirect |
| 293. C5 | #68516 | semidirect |
| 306. C3 | #10598942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750931 | 2 |
| C4×#6659 | 2 |
| #11746998 | 2 |
| C5×#4483 | 2 |
| C3×#64700 | 2 |
| #11745844 | 2 |
| C3⋊C8×#168 | 2 |
| #10598942 | 3 |
| #68516 | 5 |