Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 6. #10602172 | C3 | direct (N × H) |
| 64. C3×C5×C8 | Q16 | semidirect |
| 127. C5×C8 | C3×Q16 | semidirect |
| 156. C3×C8 | #689 | semidirect |
| 178. C3×C5 | #1694 | semidirect |
| 202. C8 | C3×#689 | semidirect |
| 206. C5 | C3×#1694 | semidirect |
| 215. C3 | #10602172 | 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×#65379 | 2 |
| C3×#64968 | 2 |
| C3×#64767 | 2 |
| C3×#64677 | 2 |
| #10602172 | 3 |
| C3×#1694 | 5 |