Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 3. #11746386 | C2 | semidirect |
| 4. C3×#64785 | C2 | semidirect |
| 5. #11745936 | C2 | semidirect |
| 6. #11745933 | C2 | semidirect |
| 24. #64785 | D3 | semidirect |
| 205. C3×C5 | #2239 | semidirect |
| 234. C5 | #69267 | semidirect |
| 243. C3 | #10601883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5189 | 2 |
| #11748059 | 2 |
| #11746386 | 2 |
| C3×#64785 | 2 |
| #11745936 | 2 |
| #11745933 | 2 |
| #11745883 | 2 |
| #10601883 | 3 |
| #69267 | 5 |