Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 110 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×#65137 | C2 | semidirect |
| 3. C3×#64968 | C2 | semidirect |
| 4. C3×C5×#334 | C2 | semidirect |
| 5. C3×#64705 | C2 | semidirect |
| 6. #10599343 | C3 | direct (N × H) |
| 19. #65137 | C2×C3 | semidirect |
| 21. #64968 | C2×C3 | semidirect |
| 22. C5×#334 | C2×C3 | semidirect |
| 23. #64705 | C2×C3 | semidirect |
| 42. C3×#334 | D5 | semidirect |
| 70. C3×C5×C8 | SD16 | semidirect |
| 101. #334 | C3×D5 | semidirect |
| 142. C5×C8 | C3×SD16 | semidirect |
| 174. C3×C8 | #677 | semidirect |
| 200. C3×C5 | #1688 | semidirect |
| 230. C8 | C3×#677 | semidirect |
| 235. C5 | C3×#1688 | semidirect |
| 246. C3 | #10599343 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65137 | 2 |
| C3×#64984 | 2 |
| C3×#64968 | 2 |
| C3×C5×#334 | 2 |
| C3×#64705 | 2 |
| #10599343 | 3 |
| C3×#1688 | 5 |