Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
436 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 234 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×#4502 | C3 | direct (N × H) |
| 9. C33×C16 | C4 | semidirect |
| 10. C32×C3⋊C16 | C4 | semidirect |
| 24. #4502 | C32 | direct (N × H) |
| 34. C32×C16 | Dic3 | semidirect |
| 35. C32×C16 | C3×C4 | semidirect |
| 36. C3×C3⋊C16 | C3×C4 | semidirect |
| 73. C3×C16 | C3×Dic3 | semidirect |
| 74. C3×C16 | C32×C4 | semidirect |
| 75. C3⋊C16 | C32×C4 | semidirect |
| 90. C33 | #346 | semidirect |
| 114. C16 | C32×Dic3 | semidirect |
| 127. C32 | #4502 | direct (N × H) |
| 128. C32 | C3×#346 | semidirect |
| 145. C3 | C3×#4502 | direct (N × H) |
| 146. C3 | C32×#346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C16 | 2 |
| C32×C8×Dic3 | 2 |
| C2×C32×C3⋊C16 | 2 |
| C32×#346 | 3 |
| C3×#4502 | 3 |