Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 100 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. C22×C5×D24 | C2 | semidirect |
| 2. #11751216 | C2 | semidirect |
| 3. C2×#90939 | C2 | semidirect |
| 4. C3×C22⋊#672 | C2 | semidirect |
| 5. #11745894 | C2 | semidirect |
| 10. C2×D120 | C22 | semidirect |
| 15. #91102 | C22 | semidirect |
| 16. C2×C3×#672 | C22 | semidirect |
| 23. C22⋊#672 | D3 | semidirect |
| 40. C5×D24 | D4 | semidirect |
| 42. C22×D24 | D5 | semidirect |
| 57. C2×#672 | C2×D3 | semidirect |
| 114. C22×C3×C5 | D16 | semidirect |
| 143. D24 | C22⋊D5 | semidirect |
| 206. C22×C5 | D48 | semidirect |
| 233. C3×C5 | #2184 | semidirect |
| 236. C22×C3 | #3958 | semidirect |
| 280. C5 | #69108 | semidirect |
| 290. C22 | #90939 | semidirect |
| 296. C3 | #10602828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D24 | 2 |
| #11751216 | 2 |
| C2×#90939 | 2 |
| C3×C22⋊#672 | 2 |
| #11745894 | 2 |
| #10602828 | 3 |
| #69108 | 5 |