Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
152 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 52 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×D228 | C2 | semidirect |
| 2. C2×C19×D12 | C2 | semidirect |
| 3. C2×C3×C19⋊C8 | C2 | semidirect |
| 4. #11744820 | C2 | direct (N × H) |
| 10. D228 | C22 | semidirect |
| 12. C19×D12 | C22 | semidirect |
| 13. C3×C19⋊C8 | C22 | semidirect |
| 17. C2×C19⋊C8 | D3 | semidirect |
| 32. C19⋊C8 | C2×D3 | semidirect |
| 33. C2×C3×C19 | D8 | semidirect |
| 45. C3×C19 | C2×D8 | semidirect |
| 47. C2×D12 | D19 | semidirect |
| 51. C2×C19 | D24 | semidirect |
| 61. D12 | C2×D19 | semidirect |
| 63. C19 | C2×D24 | semidirect |
| 83. C2×C3 | #64525 | semidirect |
| 94. C3 | C2×#64525 | semidirect |
| 97. C2 | #11744820 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D228 | 2 |
| C2×C19×D12 | 2 |
| C2×C3×C19⋊C8 | 2 |
| #11744820 | 2 |
| C2×#64525 | 3 |
| C2×D24 | 19 |