Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
148 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 148 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 |
|---|---|---|
| 2. C2×C19×Dic6 | C2 | semidirect |
| 3. C3×C4⋊C4×C19 | C2 | semidirect |
| 6. C19×Dic3⋊C4 | C2 | semidirect |
| 7. C19×Dic3⋊C4 | C2 | semidirect |
| 22. C4⋊C4×C19 | D3 | semidirect |
| 28. C2×D3×C19 | Q8 | semidirect |
| 48. #896 | C19 | direct (N × H) |
| 59. C3×C19 | C22⋊Q8 | semidirect |
| 61. C2×Dic6 | C2×C19 | semidirect |
| 62. C3×C4⋊C4 | C2×C19 | semidirect |
| 65. Dic3⋊C4 | C2×C19 | semidirect |
| 66. Dic3⋊C4 | C2×C19 | semidirect |
| 81. C19 | #896 | direct (N × H) |
| 86. C4⋊C4 | D3×C19 | semidirect |
| 92. C2×D3 | Q8×C19 | semidirect |
| 122. C3 | C19×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C19 | 2 |
| C2×C19×Dic6 | 2 |
| C3×C4⋊C4×C19 | 2 |
| C19×(C2×D3)⋊C4 | 2 |
| C19×Dic3⋊C4 | 2 |
| C19×C22⋊Q8 | 3 |
| #896 | 19 |