Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C4×D57 | C2 | semidirect |
| 2. C2×C4×D3×C19 | C2 | semidirect |
| 4. C3×C4×Dic19 | C2 | semidirect |
| 5. Dic19⋊Dic3 | C2 | semidirect |
| 6. #11744833 | C2 | semidirect |
| 7. (C2×D3)⋊Dic19 | C2 | semidirect |
| 18. #90697 | C4 | direct (N × H) |
| 25. C4×Dic19 | D3 | semidirect |
| 29. C2×D57 | C2×C4 | semidirect |
| 32. C2×D3×C19 | C2×C4 | semidirect |
| 33. C3×C4×C19 | D4 | semidirect |
| 36. C3×Dic19 | C2×C4 | semidirect |
| 62. C4×C19 | D12 | semidirect |
| 65. Dic19 | C4×D3 | semidirect |
| 66. C3×C19 | C4×D4 | semidirect |
| 69. C2×C4×D3 | D19 | semidirect |
| 90. C19 | C4×D12 | semidirect |
| 104. C2×D3 | C4×D19 | semidirect |
| 107. C3×C4 | C22⋊D19 | semidirect |
| 136. C4 | #90697 | direct (N × H) |
| 137. C3 | C4×C22⋊D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D57 | 2 |
| C2×C4×D3×C19 | 2 |
| C2×#90697 | 2 |
| C3×C4×Dic19 | 2 |
| Dic19⋊Dic3 | 2 |
| #11744833 | 2 |
| (C2×D3)⋊Dic19 | 2 |
| C4×C22⋊D19 | 3 |
| C4×D12 | 19 |