Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 132 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×#65702 | C2 | semidirect |
| 3. C3×#64882 | C2 | semidirect |
| 4. C3×C8×#170 | C2 | semidirect |
| 5. C3×#64871 | C2 | semidirect |
| 6. #10604059 | C3 | direct (N × H) |
| 18. #65702 | C2×C3 | semidirect |
| 20. #64882 | C2×C3 | semidirect |
| 21. C8×#170 | C2×C3 | semidirect |
| 22. #64871 | C2×C3 | semidirect |
| 35. C3×D40 | C8 | semidirect |
| 58. C3×D20 | C2×C8 | semidirect |
| 64. C3×#170 | D8 | semidirect |
| 65. C3×C5×C8 | C2×C8 | semidirect |
| 89. D40 | C3×C8 | semidirect |
| 124. D20 | C2×C3×C8 | semidirect |
| 130. #170 | C3×D8 | semidirect |
| 131. C5×C8 | C2×C3×C8 | semidirect |
| 161. C3×C8 | D5⋊C8 | semidirect |
| 185. C3×C5 | C8×D8 | semidirect |
| 214. C8 | C3×D5⋊C8 | semidirect |
| 219. C5 | C3×C8×D8 | semidirect |
| 230. C3 | #10604059 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65702 | 2 |
| C3×#65161 | 2 |
| C3×#64882 | 2 |
| C3×C8×#170 | 2 |
| C3×#64871 | 2 |
| #10604059 | 3 |
| C3×C8×D8 | 5 |