Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #11746721 | C2 | semidirect |
| 4. C3×#64850 | C2 | semidirect |
| 5. #11746476 | C2 | semidirect |
| 12. C16×D15 | C4 | semidirect |
| 13. C5×D3×C16 | C4 | semidirect |
| 15. #90933 | C4 | semidirect |
| 16. D3×#672 | C4 | semidirect |
| 22. #64850 | D3 | semidirect |
| 79. D3×C16 | AGL(1,𝔽5) | semidirect |
| 191. C3×C5 | #2158 | semidirect |
| 223. C5 | #69345 | semidirect |
| 234. C3 | #10604107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751658 | 2 |
| D3×D5×C16 | 2 |
| #11746721 | 2 |
| C3×#64850 | 2 |
| #11746476 | 2 |
| #10604107 | 3 |
| #69345 | 5 |