Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
456 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 2. #11722189 | C2 | semidirect |
| 3. C2×C32×C3⋊C16 | C2 | semidirect |
| 19. C2×C3×C3⋊C16 | D3 | semidirect |
| 57. C2×C3⋊C16 | C3⋊D3 | semidirect |
| 114. C33 | #359 | semidirect |
| 164. C32 | #4510 | semidirect |
| 165. C32 | #4567 | semidirect |
| 188. C3 | #10589121 | semidirect |
| 189. C3 | #10589376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64113 | 2 |
| #11722189 | 2 |
| C2×C32×C3⋊C16 | 2 |
| #10589376 | 3 |
| #10589121 | 3 |