Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
360 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 6. #10602153 | C3 | direct (N × H) |
| 57. C3×#168 | Q16 | semidirect |
| 109. #168 | C3×Q16 | semidirect |
| 149. C3×C5 | #1707 | semidirect |
| 172. C5 | C3×#1707 | semidirect |
| 179. C3 | #10602153 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| C3×#65370 | 2 |
| C3×#65368 | 2 |
| C3×#64988 | 2 |
| C3×C8×#168 | 2 |
| #10602153 | 3 |
| C3×#1707 | 5 |