Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1044 conjugacy classes of subgroups; only the 450 normal subgroups are shown.
This group has 1044 conjugacy classes of subgroups — too many to draw. Only its 450 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 |
|---|---|---|
| 5. C3×C9×Dic6 | C3 | direct (N × H) |
| 15. C33×C9 | Q8 | semidirect |
| 17. C32×Dic6 | C9 | direct (N × H) |
| 20. C9×Dic6 | C32 | direct (N × H) |
| 43. C32×C9 | Dic6 | direct (N × H) |
| 44. C32×C9 | C3×Q8 | semidirect |
| 47. C3×Dic6 | C3×C9 | direct (N × H) |
| 75. C33 | Q8×C9 | semidirect |
| 80. C3×C9 | C3×Dic6 | direct (N × H) |
| 81. C3×C9 | C32×Q8 | semidirect |
| 84. Dic6 | C32×C9 | direct (N × H) |
| 105. C32 | C9×Dic6 | direct (N × H) |
| 106. C32 | C3×Q8×C9 | semidirect |
| 110. C9 | C32×Dic6 | direct (N × H) |
| 121. C3 | C3×C9×Dic6 | direct (N × H) |
| 122. C3 | C32×Q8×C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×C9 | 2 |
| C32×C9×Dic3 | 2 |
| C33×Dic6 | 3 |
| C32×Q8×C9 | 3 |
| C3×C9×Dic6 | 3 |