Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
384 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 140 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. C3×C4×C92 | C2 | semidirect |
| 3. C3×C9×Dic9 | C2 | semidirect |
| 6. C4×C9×D9 | C3 | direct (N × H) |
| 8. C3×C9×D9 | C4 | direct (N × H) |
| 18. C4×C92 | C2×C3 | semidirect |
| 19. C9×Dic9 | C2×C3 | semidirect |
| 20. C3×C92 | C2×C4 | semidirect |
| 24. C3×C4×D9 | C9 | direct (N × H) |
| 33. C9×D9 | C3×C4 | direct (N × H) |
| 48. C3×C4×C9 | D9 | direct (N × H) |
| 49. C3×C4×C9 | C2×C9 | semidirect |
| 53. C3×Dic9 | C2×C9 | semidirect |
| 59. C92 | C2×C3×C4 | semidirect |
| 64. C4×D9 | C3×C9 | direct (N × H) |
| 79. C3×D9 | C4×C9 | direct (N × H) |
| 99. C4×C9 | C3×D9 | direct (N × H) |
| 100. C4×C9 | C2×C3×C9 | semidirect |
| 101. Dic9 | C2×C3×C9 | semidirect |
| 109. C3×C9 | C4×D9 | direct (N × H) |
| 110. C3×C9 | C2×C4×C9 | semidirect |
| 131. D9 | C3×C4×C9 | direct (N × H) |
| 139. C3×C4 | C9×D9 | direct (N × H) |
| 152. C9 | C3×C4×D9 | direct (N × H) |
| 153. C9 | C2×C3×C4×C9 | semidirect |
| 165. C4 | C3×C9×D9 | direct (N × H) |
| 168. C3 | C4×C9×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×D9 | 2 |
| C3×C4×C92 | 2 |
| C3×C9×Dic9 | 2 |
| C3×C4×D3×C9 | 3 |
| C32×C4×D9 | 3 |
| C4×C9×D9 | 3 |