Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
568 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×#91231 | C2 | semidirect |
| 3. C2×C3×#4002 | C2 | semidirect |
| 4. #11746505 | C2 | direct (N × H) |
| 18. #91231 | C22 | semidirect |
| 20. C3×#4002 | C22 | semidirect |
| 24. C2×#4002 | D3 | semidirect |
| 67. #4002 | C2×D3 | semidirect |
| 208. C2×C3×C5 | #329 | semidirect |
| 273. C3×C5 | C2×#329 | semidirect |
| 289. C2×C5 | #4464 | semidirect |
| 316. C2×C3 | #64927 | semidirect |
| 321. C5 | C2×#4464 | semidirect |
| 337. C3 | C2×#64927 | semidirect |
| 339. C2 | #11746505 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91375 | 2 |
| C2×#91231 | 2 |
| C2×C3×#4002 | 2 |
| #11746505 | 2 |
| C2×#64927 | 3 |
| C2×#4464 | 5 |