Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 124 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. C19×#235 | C2 | semidirect |
| 3. C19×#216 | C2 | semidirect |
| 4. C19×#215 | C2 | semidirect |
| 5. C19×#214 | C2 | semidirect |
| 6. C19×#213 | C2 | semidirect |
| 7. C2×C19×C3⋊C8 | C2 | semidirect |
| 21. #41×C19 | D3 | semidirect |
| 49. #950 | C19 | direct (N × H) |
| 57. C3×C19 | #135 | semidirect |
| 58. C3×#41 | C2×C19 | semidirect |
| 59. #235 | C2×C19 | semidirect |
| 60. #216 | C2×C19 | semidirect |
| 61. #215 | C2×C19 | semidirect |
| 62. #214 | C2×C19 | semidirect |
| 63. #213 | C2×C19 | semidirect |
| 64. C2×C3⋊C8 | C2×C19 | semidirect |
| 81. C19 | #950 | direct (N × H) |
| 83. #41 | D3×C19 | semidirect |
| 118. C3 | C19×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#41×C19 | 2 |
| C19×#235 | 2 |
| C19×#216 | 2 |
| C19×#215 | 2 |
| C19×#214 | 2 |
| C19×#213 | 2 |
| C2×C19×C3⋊C8 | 2 |
| C19×#135 | 3 |
| #950 | 19 |