Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
560 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 132 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. #11750796 | C2 | semidirect |
| 2. C5×#4695 | C2 | semidirect |
| 3. #11747029 | C2 | semidirect |
| 4. C3×C8×#168 | C2 | semidirect |
| 17. C8×#168 | D3 | semidirect |
| 30. #4695 | D5 | semidirect |
| 48. C3×C5×C8 | D8 | semidirect |
| 49. C3×#168 | D8 | semidirect |
| 96. C5×C8 | D24 | semidirect |
| 97. #168 | D24 | semidirect |
| 118. C3×C8 | #686 | semidirect |
| 136. C3×C5 | #1712 | semidirect |
| 157. C8 | #6654 | semidirect |
| 162. C5 | #68062 | semidirect |
| 170. C3 | #10602069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750796 | 2 |
| C5×#4695 | 2 |
| #11747029 | 2 |
| C3×C8×#168 | 2 |
| #10602069 | 3 |
| #68062 | 5 |