Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 92 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×#65740 | C2 | semidirect |
| 2. C3×#65732 | C2 | semidirect |
| 4. C3×#64909 | C2 | semidirect |
| 5. C3×#64905 | C2 | semidirect |
| 6. C3×#64851 | C2 | semidirect |
| 7. C3×#64844 | C2 | semidirect |
| 8. #10604129 | C3 | direct (N × H) |
| 19. C3×C5×SD32 | C4 | semidirect |
| 20. C3×#3961 | C4 | semidirect |
| 21. C3×#3958 | C4 | semidirect |
| 22. C3×#3932 | C4 | semidirect |
| 25. #65740 | C2×C3 | semidirect |
| 26. #65732 | C2×C3 | semidirect |
| 28. #64909 | C2×C3 | semidirect |
| 29. #64905 | C2×C3 | semidirect |
| 30. #64851 | C2×C3 | semidirect |
| 31. #64844 | C2×C3 | semidirect |
| 69. C5×SD32 | C3×C4 | semidirect |
| 70. #3961 | C3×C4 | semidirect |
| 71. #3958 | C3×C4 | semidirect |
| 72. #3932 | C3×C4 | semidirect |
| 97. C3×SD32 | AGL(1,𝔽5) | semidirect |
| 183. SD32 | C3×AGL(1,𝔽5) | semidirect |
| 240. C3×C5 | #2179 | semidirect |
| 273. C5 | C3×#2179 | semidirect |
| 282. C3 | #10604129 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65740 | 2 |
| C3×#65732 | 2 |
| C3×#65205 | 2 |
| C3×#64909 | 2 |
| C3×#64905 | 2 |
| C3×#64851 | 2 |
| C3×#64844 | 2 |
| #10604129 | 3 |
| C3×#2179 | 5 |