Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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×C19×D12 | C2 | semidirect |
| 2. C3×#64541 | C2 | semidirect |
| 3. #11744885 | C2 | semidirect |
| 4. #11744822 | C2 | semidirect |
| 5. #11744818 | C2 | semidirect |
| 12. C3×D76 | C22 | semidirect |
| 14. C3×Dic38 | C22 | semidirect |
| 15. C3⋊(C19⋊C8) | C22 | semidirect |
| 17. #64541 | D3 | semidirect |
| 33. D76 | C2×D3 | semidirect |
| 35. Dic38 | C2×D3 | semidirect |
| 49. C3×C19 | AGL(1,ℤ/8) | semidirect |
| 51. C2×D12 | D19 | semidirect |
| 69. C19 | #949 | semidirect |
| 102. C3 | #10597378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C19×D12 | 2 |
| C3×#64541 | 2 |
| #11744885 | 2 |
| #11744822 | 2 |
| #11744818 | 2 |
| #10597378 | 3 |
| #949 | 19 |