Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 122 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. C3×#65485 | C2 | semidirect |
| 3. C3×#64787 | C2 | semidirect |
| 4. C3×#64726 | C2 | semidirect |
| 5. C3×#64722 | C2 | semidirect |
| 6. #10602305 | C3 | direct (N × H) |
| 9. C3×C5×Q32 | C4 | semidirect |
| 10. C3×C5×SD32 | C4 | semidirect |
| 11. C3×C5×D16 | C4 | semidirect |
| 19. #65485 | C2×C3 | semidirect |
| 20. #64787 | C2×C3 | semidirect |
| 21. #64726 | C2×C3 | semidirect |
| 22. #64722 | C2×C3 | semidirect |
| 43. C5×Q32 | C3×C4 | semidirect |
| 44. C5×SD32 | C3×C4 | semidirect |
| 45. C5×D16 | C3×C4 | semidirect |
| 64. C3×Q32 | Dic5 | semidirect |
| 65. C3×SD32 | Dic5 | semidirect |
| 66. C3×D16 | Dic5 | semidirect |
| 121. Q32 | C3×Dic5 | semidirect |
| 122. SD32 | C3×Dic5 | semidirect |
| 123. D16 | C3×Dic5 | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | C3×#2179 | semidirect |
| 191. C3 | #10602305 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#508 | 2 |
| C3×#65485 | 2 |
| C3×#64787 | 2 |
| C3×#64726 | 2 |
| C3×#64722 | 2 |
| #10602305 | 3 |
| C3×#2179 | 5 |