Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
214 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 1. C32×D48 | C2 | semidirect |
| 2. C3×C3⋊(C3⋊C32) | C2 | semidirect |
| 4. #10589070 | C3 | direct (N × H) |
| 9. C3×D48 | D3 | semidirect |
| 10. C3×D48 | C2×C3 | semidirect |
| 11. C3⋊(C3⋊C32) | C2×C3 | semidirect |
| 32. D48 | C3×D3 | semidirect |
| 68. C33 | D32 | semidirect |
| 101. C32 | #4519 | semidirect |
| 102. C32 | C3×D32 | semidirect |
| 119. C3 | #10589070 | direct (N × H) |
| 120. C3 | C3×#4519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D48 | 2 |
| C3×C3⋊(C3⋊C32) | 2 |
| C3×#4519 | 3 |
| #10589070 | 3 |