Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11747851 | C2 | semidirect |
| 4. C2×#90948 | C2 | semidirect |
| 5. C5×#4503 | C2 | semidirect |
| 6. C3×#64721 | C2 | semidirect |
| 28. #64721 | D3 | semidirect |
| 56. #4503 | D5 | semidirect |
| 238. C3×C5 | #2211 | semidirect |
| 274. C5 | #69294 | semidirect |
| 286. C3 | #10600030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91084 | 2 |
| #11747965 | 2 |
| #11747851 | 2 |
| C2×#90948 | 2 |
| C5×#4503 | 2 |
| C3×#64721 | 2 |
| #11745896 | 2 |
| #10600030 | 3 |
| #69294 | 5 |