Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 103 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. C3×C5×#446 | C2 | semidirect |
| 3. #11751121 | C2 | semidirect |
| 6. #11746303 | C2 | semidirect |
| 7. #11746279 | C2 | semidirect |
| 25. C5×#446 | D3 | semidirect |
| 51. C3×#446 | D5 | semidirect |
| 92. C3×C5×C8 | SD16 | semidirect |
| 132. #446 | D15 | semidirect |
| 185. C5×C8 | #215 | semidirect |
| 225. C3×C8 | #688 | semidirect |
| 259. C3×C5 | #1686 | semidirect |
| 296. C8 | #6717 | semidirect |
| 301. C5 | #70958 | semidirect |
| 314. C3 | #10601751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#446 | 2 |
| #11751128 | 2 |
| #11751121 | 2 |
| #11750794 | 2 |
| #11746306 | 2 |
| #11746303 | 2 |
| #11746279 | 2 |
| #10601751 | 3 |
| #70958 | 5 |