Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 39. #6718 | C8 | semidirect |
| 85. C3⋊#170 | Q16 | semidirect |
| 237. C3×C5 | C8×Q16 | semidirect |
| 272. C5 | #68213 | semidirect |
| 283. C3 | #10603968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊#170 | 2 |
| #11751783 | 2 |
| #11749244 | 2 |
| C3×Q8⋊#170 | 2 |
| #11746515 | 2 |
| #11746495 | 2 |
| C3⋊C8×#170 | 2 |
| #10603968 | 3 |
| #68213 | 5 |