Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 116 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×#65774 | C2 | semidirect |
| 3. C3×D4⋊#170 | C2 | semidirect |
| 4. C3×#64882 | C2 | semidirect |
| 5. C3×C8×#170 | C2 | semidirect |
| 6. #10604795 | C3 | direct (N × H) |
| 18. #65774 | C2×C3 | semidirect |
| 20. D4⋊#170 | C2×C3 | semidirect |
| 21. #64882 | C2×C3 | semidirect |
| 22. C8×#170 | C2×C3 | semidirect |
| 64. C3×#170 | D8 | semidirect |
| 65. C3×C5×C8 | M16 | semidirect |
| 130. #170 | C3×D8 | semidirect |
| 131. C5×C8 | C3×M16 | semidirect |
| 161. C3×C8 | #704 | semidirect |
| 185. C3×C5 | #1589 | semidirect |
| 214. C8 | C3×#704 | semidirect |
| 219. C5 | C3×#1589 | semidirect |
| 230. C3 | #10604795 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65774 | 2 |
| C3×D8×Dic5 | 2 |
| C3×D4⋊#170 | 2 |
| C3×#64882 | 2 |
| C3×C8×#170 | 2 |
| #10604795 | 3 |
| C3×#1589 | 5 |