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. #11756512 | C2 | semidirect |
| 2. C5×#5752 | C2 | semidirect |
| 3. C3×#65429 | C2 | semidirect |
| 4. #11747563 | C2 | semidirect |
| 5. C2×#90944 | C2 | semidirect |
| 6. #11747547 | C2 | semidirect |
| 7. #11747546 | C2 | semidirect |
| 13. C2×Dic60 | C22 | semidirect |
| 14. #91793 | C22 | semidirect |
| 18. C3×#3944 | C22 | semidirect |
| 19. C2×C3×#672 | C22 | semidirect |
| 20. #90948 | C22 | semidirect |
| 21. #90945 | C22 | semidirect |
| 22. #90944 | C22 | semidirect |
| 23. #90944 | C22 | semidirect |
| 24. #90939 | C22 | semidirect |
| 32. #65429 | D3 | semidirect |
| 55. #5752 | D5 | semidirect |
| 75. #3944 | C2×D3 | semidirect |
| 76. C2×#672 | C2×D3 | semidirect |
| 251. C3×C5 | #3416 | semidirect |
| 285. C5 | #82014 | semidirect |
| 294. C3 | #10615739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756512 | 2 |
| C5×#5752 | 2 |
| C3×#65429 | 2 |
| #11747563 | 2 |
| C2×#90944 | 2 |
| #11747547 | 2 |
| #11747546 | 2 |
| #10615739 | 3 |
| #82014 | 5 |