Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
312 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 114 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. #10602170 | C3 | direct (N × H) |
| 65. C3×C5×C8 | Q16 | semidirect |
| 130. C5×C8 | C3×Q16 | semidirect |
| 160. C3×C8 | #689 | semidirect |
| 183. C3×C5 | #1674 | semidirect |
| 209. C8 | C3×#689 | semidirect |
| 213. C5 | C3×#1674 | semidirect |
| 223. C3 | #10602170 | 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×C8×Dic10 | 2 |
| C3×#64767 | 2 |
| C3×#64678 | 2 |
| #10602170 | 3 |
| C3×#1674 | 5 |