Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
292 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 84 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. #11751740 | C2 | semidirect |
| 2. #11751736 | C2 | semidirect |
| 4. #11746732 | C2 | semidirect |
| 5. C3×C4×#674 | C2 | semidirect |
| 6. #11746553 | C2 | semidirect |
| 7. #11746551 | C2 | semidirect |
| 31. C4×#674 | D3 | semidirect |
| 240. C3×C5 | #2170 | semidirect |
| 273. C5 | #69056 | semidirect |
| 282. C3 | #10603999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751740 | 2 |
| #11751736 | 2 |
| #11747018 | 2 |
| #11746732 | 2 |
| C3×C4×#674 | 2 |
| #11746553 | 2 |
| #11746551 | 2 |
| #10603999 | 3 |
| #69056 | 5 |