Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1988 conjugacy classes of subgroups; only the 871 normal subgroups are shown.
This group has 1988 conjugacy classes of subgroups — too many to draw. Only its 871 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 |
|---|---|---|
| 4. #11722185 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 9. C33×M16 | C4 | semidirect |
| 14. #88855 | C4 | semidirect |
| 29. C33×C8 | C2×C4 | semidirect |
| 30. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 34. C32×M16 | Dic3 | semidirect |
| 48. C3⋊(C3⋊Dic3) | M16 | direct (N × H) |
| 62. C32×C8 | C2×Dic3 | semidirect |
| 70. C3×M16 | C3⋊Dic3 | semidirect |
| 90. C33 | C4×M16 | semidirect |
| 99. C3×C8 | C2×C3⋊Dic3 | semidirect |
| 107. M16 | C3⋊(C3⋊Dic3) | direct (N × H) |
| 121. C32 | Dic3×M16 | semidirect |
| 131. C8 | C2×C3⋊(C3⋊Dic3) | semidirect |
| 143. C3 | M16×C3⋊Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| C2×#88855 | 2 |
| #11722185 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| M16×C3⋊Dic3 | 3 |