Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 138 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×#64983 | C2 | semidirect |
| 3. C3×#64982 | C2 | semidirect |
| 4. C3×#64969 | C2 | semidirect |
| 5. C3×C5×#322 | C2 | semidirect |
| 6. #10598884 | C3 | direct (N × H) |
| 18. #64983 | C2×C3 | semidirect |
| 19. #64982 | C2×C3 | semidirect |
| 20. #64969 | C2×C3 | semidirect |
| 21. C5×#322 | C2×C3 | semidirect |
| 38. C3×#322 | D5 | semidirect |
| 60. C3×C5×C8 | SD16 | semidirect |
| 86. #322 | C3×D5 | semidirect |
| 118. C5×C8 | C3×SD16 | semidirect |
| 143. C3×C8 | #677 | semidirect |
| 164. C3×C5 | #1715 | semidirect |
| 188. C8 | C3×#677 | semidirect |
| 193. C5 | C3×#1715 | semidirect |
| 202. C3 | #10598884 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64984 | 2 |
| C3×#64983 | 2 |
| C3×#64982 | 2 |
| C3×#64969 | 2 |
| C3×C5×#322 | 2 |
| #10598884 | 3 |
| C3×#1715 | 5 |