Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1484 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 1484 conjugacy classes of subgroups — too many to draw. Only its 365 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 |
|---|---|---|
| 3. C33×#108 | C2 | semidirect |
| 4. #11722192 | C2 | semidirect |
| 5. #11722189 | C2 | semidirect |
| 18. C32×#108 | D3 | semidirect |
| 52. C3×#108 | C3⋊D3 | semidirect |
| 70. C3⋊(C3⋊D3) | #108 | direct (N × H) |
| 92. #108 | C3⋊(C3⋊D3) | direct (N × H) |
| 93. C33 | C2×#108 | semidirect |
| 126. C32 | D3×#108 | semidirect |
| 150. C3 | C3⋊D3×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×C3⋊(C3⋊D3) | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C33×#108 | 2 |
| #11722192 | 2 |
| #11722189 | 2 |
| C3⋊D3×#108 | 3 |