Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 110 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. #11752417 | C2 | semidirect |
| 3. C3×C4×#704 | C2 | semidirect |
| 4. #11746493 | C2 | semidirect |
| 5. #11746489 | C2 | semidirect |
| 27. C4×#704 | D3 | semidirect |
| 93. C5×D12 | M16 | semidirect |
| 96. C5×Dic6 | M16 | semidirect |
| 274. D12 | #704 | semidirect |
| 280. Dic6 | #704 | semidirect |
| 330. C3×C5 | #1489 | semidirect |
| 386. C5 | #69854 | semidirect |
| 405. C3 | #10605003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic5×#235 | 2 |
| #11752417 | 2 |
| C3×C4×#704 | 2 |
| #11746493 | 2 |
| #11746489 | 2 |
| #10605003 | 3 |
| #69854 | 5 |