Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
304 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 87. C3×#168 | Q16 | semidirect |
| 173. #168 | #216 | semidirect |
| 237. C3×C5 | #1591 | semidirect |
| 272. C5 | #70951 | semidirect |
| 283. C3 | #10599018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6718 | 2 |
| C3×#65313 | 2 |
| #11746864 | 2 |
| C5×#4535 | 2 |
| #11745868 | 2 |
| #11745844 | 2 |
| C3⋊C8×#168 | 2 |
| #10599018 | 3 |
| #70951 | 5 |