Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
456 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 150 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. C33×#108 | C2 | semidirect |
| 3. C2×C32×C3⋊C16 | C2 | semidirect |
| 5. C3×#4497 | C3 | direct (N × H) |
| 17. C32×#108 | D3 | semidirect |
| 18. C32×#108 | C2×C3 | semidirect |
| 19. C2×C3×C3⋊C16 | C2×C3 | semidirect |
| 29. #4497 | C32 | direct (N × H) |
| 55. C3×#108 | C3×D3 | semidirect |
| 56. C3×#108 | C2×C32 | semidirect |
| 57. C2×C3⋊C16 | C2×C32 | semidirect |
| 113. #108 | C32×D3 | semidirect |
| 114. C33 | #359 | semidirect |
| 164. C32 | #4497 | direct (N × H) |
| 165. C32 | C3×#359 | semidirect |
| 188. C3 | C3×#4497 | direct (N × H) |
| 189. C3 | C32×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#904 | 2 |
| C33×#108 | 2 |
| C2×C32×C3⋊C16 | 2 |
| C32×#359 | 3 |
| C3×#4497 | 3 |