Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. C2×C3×C4×D19 | C2 | semidirect |
| 3. C2×Dic3×D19 | C2 | semidirect |
| 4. #11744889 | C2 | semidirect |
| 5. C19×(C2×D3)⋊C4 | C2 | semidirect |
| 6. #11744833 | C2 | semidirect |
| 7. (C2×D3)⋊Dic19 | C2 | semidirect |
| 14. C2×D3×D19 | C4 | semidirect |
| 15. C2×C3×C4×C19 | C22 | semidirect |
| 16. C2×Dic57 | C22 | semidirect |
| 17. C2×Dic3×C19 | C22 | semidirect |
| 18. C2×C3×Dic19 | C22 | semidirect |
| 23. C2×C4×D19 | D3 | semidirect |
| 31. C2×D57 | C2×C4 | semidirect |
| 34. C2×D3×C19 | C2×C4 | semidirect |
| 50. C2×C4×C19 | C2×D3 | semidirect |
| 52. C2×Dic19 | C2×D3 | semidirect |
| 59. C3×D19 | C22⋊C4 | semidirect |
| 77. C3×C19 | C2×C22⋊C4 | semidirect |
| 84. (C2×D3)⋊C4 | D19 | direct (N × H) |
| 90. D19 | (C2×D3)⋊C4 | direct (N × H) |
| 100. C2×C3×C4 | C2×D19 | semidirect |
| 103. C2×Dic3 | C2×D19 | semidirect |
| 104. C19 | C2×(C2×D3)⋊C4 | semidirect |
| 122. C2×D3 | C4×D19 | semidirect |
| 138. C2×C4 | D3×D19 | semidirect |
| 160. C3 | C22⋊C4×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×D19 | 2 |
| C2×C3×C4×D19 | 2 |
| C2×Dic3×D19 | 2 |
| #11744889 | 2 |
| C19×(C2×D3)⋊C4 | 2 |
| #11744833 | 2 |
| (C2×D3)⋊Dic19 | 2 |
| C22⋊C4×D19 | 3 |
| C2×(C2×D3)⋊C4 | 19 |