Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
264 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4×D57 | C2 | semidirect |
| 3. C3×C22⋊C4×C19 | C2 | semidirect |
| 4. #11744894 | C2 | semidirect |
| 5. #11744889 | C2 | semidirect |
| 9. C22×D57 | C4 | semidirect |
| 12. C2×C3×C4×C19 | C22 | semidirect |
| 13. C2×Dic57 | C22 | semidirect |
| 17. C22⋊C4×C19 | D3 | semidirect |
| 21. C22×C3×C19 | C2×C4 | semidirect |
| 26. C2×D57 | C2×C4 | semidirect |
| 35. C2×C4×C19 | C2×D3 | semidirect |
| 42. D57 | C22⋊C4 | direct (N × H) |
| 45. C22×C19 | C4×D3 | semidirect |
| 54. C3×C19 | C2×C22⋊C4 | semidirect |
| 57. C3×C22⋊C4 | D19 | semidirect |
| 71. C2×C3×C4 | C2×D19 | semidirect |
| 74. C19 | D3×C22⋊C4 | semidirect |
| 79. C22⋊C4 | D57 | direct (N × H) |
| 81. C22×C3 | C4×D19 | semidirect |
| 97. C2×C4 | C2×D57 | semidirect |
| 109. C22 | C4×D57 | semidirect |
| 113. C3 | C22⋊C4×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D57 | 2 |
| C2×C4×D57 | 2 |
| C3×C22⋊C4×C19 | 2 |
| #11744894 | 2 |
| #11744889 | 2 |
| C22⋊C4×D19 | 3 |
| D3×C22⋊C4 | 19 |