Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 70 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. C3×#65201 | C2 | semidirect |
| 2. C3×D5×D16 | C2 | semidirect |
| 3. C3×C5×D32 | C2 | semidirect |
| 4. C3×#64740 | C2 | semidirect |
| 5. C3×#64739 | C2 | semidirect |
| 6. C3×#64669 | C2 | semidirect |
| 7. C3×#64667 | C2 | semidirect |
| 8. #10600170 | C3 | direct (N × H) |
| 12. C3×C5×D16 | C22 | semidirect |
| 15. C3×Dic40 | C22 | semidirect |
| 18. C3×C5×C32 | C22 | semidirect |
| 19. C3×#3926 | C22 | semidirect |
| 21. #65201 | C2×C3 | semidirect |
| 22. D5×D16 | C2×C3 | semidirect |
| 23. C5×D32 | C2×C3 | semidirect |
| 24. #64740 | C2×C3 | semidirect |
| 25. #64739 | C2×C3 | semidirect |
| 26. #64669 | C2×C3 | semidirect |
| 27. #64667 | C2×C3 | semidirect |
| 44. C3×D32 | D5 | semidirect |
| 49. C5×D16 | C22×C3 | semidirect |
| 52. Dic40 | C22×C3 | semidirect |
| 55. C5×C32 | C22×C3 | semidirect |
| 56. #3926 | C22×C3 | semidirect |
| 76. C3×D16 | C2×D5 | semidirect |
| 79. C3×C32 | C2×D5 | semidirect |
| 96. D32 | C3×D5 | semidirect |
| 135. D16 | C2×C3×D5 | semidirect |
| 138. C32 | C2×C3×D5 | semidirect |
| 174. C3×C5 | #2263 | semidirect |
| 204. C5 | C3×#2263 | semidirect |
| 213. C3 | #10600170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65201 | 2 |
| C3×D5×D16 | 2 |
| C3×C5×D32 | 2 |
| C3×#64740 | 2 |
| C3×#64739 | 2 |
| C3×#64669 | 2 |
| C3×#64667 | 2 |
| #10600170 | 3 |
| C3×#2263 | 5 |