Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
680 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 1. C3×#66256 | C2 | semidirect |
| 3. #11752436 | C2 | semidirect |
| 4. C2×#91174 | C2 | semidirect |
| 5. #11746576 | C2 | semidirect |
| 27. #66256 | D3 | semidirect |
| 56. C3×#704 | D4 | semidirect |
| 170. #704 | #67 | semidirect |
| 401. C3×C5 | #1914 | semidirect |
| 472. C5 | #72030 | semidirect |
| 495. C3 | #10604464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66256 | 2 |
| #11754940 | 2 |
| #11752436 | 2 |
| C2×#91174 | 2 |
| #11746576 | 2 |
| #10604464 | 3 |
| #72030 | 5 |