Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1140 conjugacy classes of subgroups; only the 392 normal subgroups are shown.
This group has 1140 conjugacy classes of subgroups — too many to draw. Only its 392 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33×C4 | D9 |
| commutator, hypocenter | C9 | C2×C33×C4 |
| Frattini | C2×C3 | C2×C33×D3 |
| Fitting | C33×C4×C9 | C2 |
| socle | C2×C34 | C2×D3 |
| prime radical | C2×C33×D9 | C2 |
| cosocle | C2×C9 | C22×C33 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C33×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C33×C4×C9 | C2 | semidirect |
| 3. C33×Dic9 | C2 | semidirect |
| 5. C32×C4×D9 | C3 | direct (N × H) |
| 7. C33×D9 | C4 | direct (N × H) |
| 13. C32×C4×C9 | C2×C3 | semidirect |
| 14. C32×Dic9 | C2×C3 | semidirect |
| 15. C33×C9 | C2×C4 | semidirect |
| 18. C3×C4×D9 | C32 | direct (N × H) |
| 23. C32×D9 | C3×C4 | direct (N × H) |
| 28. C33×C4 | D9 | direct (N × H) |
| 33. C3×C4×C9 | C2×C32 | semidirect |
| 34. C3×Dic9 | C2×C32 | semidirect |
| 37. C32×C9 | C2×C3×C4 | semidirect |
| 40. C4×D9 | C33 | direct (N × H) |
| 48. C3×D9 | C32×C4 | direct (N × H) |
| 53. C32×C4 | C3×D9 | direct (N × H) |
| 58. C4×C9 | C2×C33 | semidirect |
| 59. Dic9 | C2×C33 | semidirect |
| 61. C33 | C4×D9 | direct (N × H) |
| 64. C3×C9 | C2×C32×C4 | semidirect |
| 74. D9 | C33×C4 | direct (N × H) |
| 79. C3×C4 | C32×D9 | direct (N × H) |
| 83. C32 | C3×C4×D9 | direct (N × H) |
| 86. C9 | C2×C33×C4 | semidirect |
| 95. C4 | C33×D9 | direct (N × H) |
| 97. C3 | C32×C4×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D9 | 2 |
| C33×C4×C9 | 2 |
| C33×Dic9 | 2 |
| C33×C4×D3 | 3 |
| C32×C4×D9 | 3 |