Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
736 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | A4×D9 |
| commutator, cosocle, hypocenter | C22×C9 | C2×C33 |
| Frattini | C3 | C32×D3×A4 |
| Fitting | C22×C32×C9 | C2×C3 |
| socle | C22×C33 | C3×D3 |
| LCS | G ▷ C22×C9 | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C9×A4 | C2 | semidirect |
| 3. C22×C32×D9 | C3 | semidirect |
| 4. C3×A4×D9 | C3 | direct (N × H) |
| 7. C22×C32×C9 | C2×C3 | semidirect |
| 12. C3×C9×A4 | C2×C3 | semidirect |
| 17. C22×C3×D9 | C32 | semidirect |
| 18. A4×D9 | C32 | direct (N × H) |
| 23. C32×D9 | A4 | direct (N × H) |
| 29. C32×A4 | D9 | direct (N × H) |
| 32. C22×C3×C9 | C2×C32 | semidirect |
| 37. C9×A4 | C2×C32 | semidirect |
| 42. C32×C9 | C2×A4 | semidirect |
| 47. C22×D9 | C33 | semidirect |
| 57. C3×D9 | C3×A4 | direct (N × H) |
| 61. C22×C32 | C3×D9 | semidirect |
| 67. C3×A4 | C3×D9 | direct (N × H) |
| 70. C22×C9 | C2×C33 | semidirect |
| 83. C3×C9 | C2×C3×A4 | semidirect |
| 99. D9 | C32×A4 | direct (N × H) |
| 103. C22×C3 | C32×D9 | semidirect |
| 108. A4 | C32×D9 | direct (N × H) |
| 114. C32 | A4×D9 | direct (N × H) |
| 118. C9 | C2×C32×A4 | semidirect |
| 130. C22 | C33×D9 | semidirect |
| 134. C3 | C3×A4×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×A4 | 2 |
| C32×D3×A4 | 3 |
| C22×C32×D9 | 3 |
| C3×A4×D9 | 3 |
| C33×D9 | 4 |