Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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×C4⋊C4×C19 | C2 | semidirect |
| 5. C4⋊Dic57 | C2 | semidirect |
| 6. #11744887 | C2 | semidirect |
| 7. C4×Dic57 | C2 | semidirect |
| 16. C4⋊C4×C19 | D3 | semidirect |
| 55. C3×C19 | #126 | semidirect |
| 56. C3×C4⋊C4 | D19 | semidirect |
| 75. C19 | #898 | semidirect |
| 78. C4⋊C4 | D57 | semidirect |
| 114. C3 | #10597344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊C4×C19 | 2 |
| #11744889 | 2 |
| C4⋊Dic57 | 2 |
| #11744887 | 2 |
| C4×Dic57 | 2 |
| #10597344 | 3 |
| #898 | 19 |