Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 2. #11746998 | C2 | semidirect |
| 3. C8×C3⋊#168 | C2 | semidirect |
| 4. C3×#64678 | C2 | semidirect |
| 5. #11745836 | C2 | semidirect |
| 21. #64678 | D3 | semidirect |
| 33. C5×D24 | C8 | semidirect |
| 58. C5×D12 | C2×C8 | semidirect |
| 62. C3×C5×C8 | C2×C8 | semidirect |
| 65. C3⋊#168 | D8 | semidirect |
| 116. D24 | #168 | semidirect |
| 128. C5×C8 | D3×C8 | semidirect |
| 153. D12 | C2×#168 | semidirect |
| 158. C3×C8 | C2×#168 | semidirect |
| 185. C3×C5 | C8×D8 | semidirect |
| 214. C8 | D3×#168 | semidirect |
| 219. C5 | #68556 | semidirect |
| 230. C3 | D8×#168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D24 | 2 |
| #11746998 | 2 |
| C8×C3⋊#168 | 2 |
| C3×#64678 | 2 |
| #11745836 | 2 |
| D8×#168 | 3 |
| #68556 | 5 |