Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 166 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. C4×C3⋊#674 | C2 | semidirect |
| 4. C3×C4×#674 | C2 | semidirect |
| 5. #11746542 | C2 | semidirect |
| 12. #91165 | C4 | direct (N × H) |
| 22. C4×#674 | D3 | semidirect |
| 34. C3⋊#674 | C2×C4 | semidirect |
| 35. C3×#674 | C2×C4 | semidirect |
| 86. #674 | C4×D3 | semidirect |
| 95. C3×C4×C5 | M32 | semidirect |
| 155. C4×C5 | #798 | semidirect |
| 171. C3×C5 | C4×M32 | semidirect |
| 175. C3×C4 | #3998 | semidirect |
| 198. C5 | C4×#798 | semidirect |
| 204. C4 | #91165 | direct (N × H) |
| 207. C3 | C4×#3998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91165 | 2 |
| C4×D3×#168 | 2 |
| C4×C3⋊#674 | 2 |
| C3×C4×#674 | 2 |
| #11746542 | 2 |
| C4×#3998 | 3 |
| C4×#798 | 5 |