Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
384 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 120 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×C3×C9×D9 | C2 | semidirect |
| 2. C3×C4×C92 | C2 | semidirect |
| 5. C9×D36 | C3 | direct (N × H) |
| 13. C2×C9×D9 | C2×C3 | semidirect |
| 15. C4×C92 | C2×C3 | semidirect |
| 16. C3×C92 | D4 | semidirect |
| 20. C3×D36 | C9 | direct (N × H) |
| 34. C2×C3×D9 | C2×C9 | semidirect |
| 42. C3×C4×C9 | D9 | semidirect |
| 43. C3×C4×C9 | C2×C9 | semidirect |
| 50. C92 | C3×D4 | semidirect |
| 55. D36 | C3×C9 | direct (N × H) |
| 81. C2×D9 | C2×C3×C9 | semidirect |
| 86. C4×C9 | C3×D9 | semidirect |
| 87. C4×C9 | C2×C3×C9 | semidirect |
| 95. C3×C9 | D36 | direct (N × H) |
| 96. C3×C9 | D4×C9 | semidirect |
| 123. C3×C4 | C9×D9 | semidirect |
| 135. C9 | C3×D36 | direct (N × H) |
| 136. C9 | C3×D4×C9 | semidirect |
| 147. C4 | C3×C9×D9 | semidirect |
| 150. C3 | C9×D36 | 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×D12 | 3 |
| C32×D36 | 3 |
| C9×D36 | 3 |