Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
268 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 68 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. #11748057 | C2 | semidirect |
| 3. #11746334 | C2 | semidirect |
| 4. C5×#4516 | C2 | semidirect |
| 5. C3×#64734 | C2 | semidirect |
| 6. #11745934 | C2 | semidirect |
| 7. #11745918 | C2 | semidirect |
| 25. #64734 | D3 | semidirect |
| 49. #4516 | D5 | semidirect |
| 213. C3×C5 | #2238 | semidirect |
| 247. C5 | #69116 | semidirect |
| 258. C3 | #10600050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11748057 | 2 |
| #11747905 | 2 |
| #11746334 | 2 |
| C5×#4516 | 2 |
| C3×#64734 | 2 |
| #11745934 | 2 |
| #11745918 | 2 |
| #10600050 | 3 |
| #69116 | 5 |