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 |
|---|---|---|
| 1. #11751297 | C2 | semidirect |
| 3. #11748070 | C2 | semidirect |
| 4. C5×#4567 | C2 | semidirect |
| 5. #11745945 | C2 | semidirect |
| 6. #11745904 | C2 | semidirect |
| 7. #11745875 | C2 | semidirect |
| 18. C3×#3961 | C4 | semidirect |
| 19. C3×#3960 | C4 | semidirect |
| 20. C3×#3959 | C4 | semidirect |
| 21. C3×#3958 | C4 | semidirect |
| 56. #4567 | D5 | semidirect |
| 66. #3961 | Dic3 | semidirect |
| 67. #3960 | Dic3 | semidirect |
| 68. #3959 | Dic3 | semidirect |
| 69. #3958 | Dic3 | semidirect |
| 240. C3×C5 | #2179 | semidirect |
| 273. C5 | #71512 | semidirect |
| 282. C3 | #10600032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751297 | 2 |
| C3×#65483 | 2 |
| #11748070 | 2 |
| C5×#4567 | 2 |
| #11745945 | 2 |
| #11745904 | 2 |
| #11745875 | 2 |
| #10600032 | 3 |
| #71512 | 5 |