Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #11746945 | C2 | semidirect |
| 4. #11746863 | C2 | semidirect |
| 5. #11746307 | C2 | semidirect |
| 6. C3×#64699 | C2 | semidirect |
| 31. #64699 | D3 | semidirect |
| 94. C3×#168 | SD16 | semidirect |
| 187. #168 | #204 | semidirect |
| 259. C3×C5 | #1686 | semidirect |
| 301. C5 | #68592 | semidirect |
| 314. C3 | #10601817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4848 | 2 |
| #11747066 | 2 |
| #11746945 | 2 |
| #11746863 | 2 |
| #11746307 | 2 |
| C3×#64699 | 2 |
| #11745853 | 2 |
| #10601817 | 3 |
| #68592 | 5 |