Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 196 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. #11756511 | C2 | semidirect |
| 2. C3×#66087 | C2 | semidirect |
| 3. C5×#5140 | C2 | semidirect |
| 4. #11747560 | C2 | semidirect |
| 5. C2×#90943 | C2 | semidirect |
| 6. #11747544 | C2 | semidirect |
| 7. #11747542 | C2 | semidirect |
| 16. C2×C3×Dic20 | C22 | semidirect |
| 17. C3×#4050 | C22 | semidirect |
| 18. C5×#812 | C22 | semidirect |
| 19. C2×C5×C3⋊C16 | C22 | semidirect |
| 20. #90947 | C22 | semidirect |
| 21. #90943 | C22 | semidirect |
| 22. #90943 | C22 | semidirect |
| 23. #90942 | C22 | semidirect |
| 24. #90938 | C22 | semidirect |
| 26. #66087 | D3 | semidirect |
| 60. #5140 | D5 | semidirect |
| 66. C2×Dic20 | C2×D3 | semidirect |
| 68. #4050 | C2×D3 | semidirect |
| 109. #812 | C2×D5 | semidirect |
| 110. C2×C3⋊C16 | C2×D5 | semidirect |
| 251. C3×C5 | #3416 | semidirect |
| 285. C5 | #84016 | semidirect |
| 294. C3 | #10613745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756511 | 2 |
| C3×#66087 | 2 |
| C5×#5140 | 2 |
| #11747560 | 2 |
| C2×#90943 | 2 |
| #11747544 | 2 |
| #11747542 | 2 |
| #10613745 | 3 |
| #84016 | 5 |