Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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×#41×C19 | C2 | semidirect |
| 2. C2×C19×D12 | C2 | semidirect |
| 3. C19×#215 | C2 | semidirect |
| 4. C19×#213 | C2 | semidirect |
| 5. C19×#208 | C2 | semidirect |
| 8. C3×Q8×C19 | C22 | semidirect |
| 10. C3×D4×C19 | C22 | semidirect |
| 15. C19×C3⋊C8 | C22 | semidirect |
| 16. #41×C19 | D3 | semidirect |
| 29. Q8×C19 | C2×D3 | semidirect |
| 33. D4×C19 | C2×D3 | semidirect |
| 41. #949 | C19 | direct (N × H) |
| 49. C3×C19 | AGL(1,ℤ/8) | semidirect |
| 50. C3×#41 | C2×C19 | semidirect |
| 51. C2×D12 | C2×C19 | semidirect |
| 52. #215 | C2×C19 | semidirect |
| 53. #213 | C2×C19 | semidirect |
| 54. #208 | C2×C19 | semidirect |
| 61. C3×Q8 | C22×C19 | semidirect |
| 63. C3×D4 | C22×C19 | semidirect |
| 68. C3⋊C8 | C22×C19 | semidirect |
| 69. C19 | #949 | direct (N × H) |
| 70. #41 | D3×C19 | semidirect |
| 83. Q8 | C2×D3×C19 | semidirect |
| 87. D4 | C2×D3×C19 | semidirect |
| 102. C3 | C19×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#41×C19 | 2 |
| C2×C19×D12 | 2 |
| C19×#215 | 2 |
| C19×#213 | 2 |
| C19×#208 | 2 |
| C19×AGL(1,ℤ/8) | 3 |
| #949 | 19 |