Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. #11748070 | C2 | semidirect |
| 3. #11746323 | C2 | semidirect |
| 4. C5×#4506 | C2 | semidirect |
| 5. #11745903 | C2 | semidirect |
| 13. C3×Dic40 | C4 | semidirect |
| 14. C3×#3932 | C4 | semidirect |
| 15. C3×D80 | C4 | semidirect |
| 39. #4506 | D5 | semidirect |
| 48. Dic40 | Dic3 | semidirect |
| 49. #3932 | Dic3 | semidirect |
| 50. D80 | Dic3 | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | #71512 | semidirect |
| 191. C3 | #10600151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65193 | 2 |
| #11748070 | 2 |
| #11746323 | 2 |
| C5×#4506 | 2 |
| #11745903 | 2 |
| #10600151 | 3 |
| #71512 | 5 |