Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
700 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 148 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. #11754008 | C2 | semidirect |
| 2. #11751002 | C2 | semidirect |
| 3. C2×C5×Dic24 | C2 | semidirect |
| 4. C3×#65193 | C2 | semidirect |
| 5. #11747550 | C2 | semidirect |
| 6. #11746841 | C2 | semidirect |
| 7. #11746839 | C2 | semidirect |
| 8. #11746831 | C2 | semidirect |
| 36. #65193 | D3 | semidirect |
| 66. C2×Dic24 | D5 | semidirect |
| 277. C3×C5 | #3417 | semidirect |
| 313. C5 | #82033 | semidirect |
| 322. C3 | #10613759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11754008 | 2 |
| #11751002 | 2 |
| C2×C5×Dic24 | 2 |
| C3×#65193 | 2 |
| #11747550 | 2 |
| #11746841 | 2 |
| #11746839 | 2 |
| #11746831 | 2 |
| #10613759 | 3 |
| #82033 | 5 |