Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3444 conjugacy classes of subgroups; only the 891 normal subgroups are shown.
This group has 3444 conjugacy classes of subgroups — too many to draw. Only its 891 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. C2×C33×C42 | C2 | semidirect |
| 3. C2×#88857 | C2 | semidirect |
| 4. #11723917 | C2 | direct (N × H) |
| 9. C33×C42 | C22 | semidirect |
| 11. #88857 | C22 | semidirect |
| 12. C2×C32×C42 | D3 | semidirect |
| 27. C32×C42 | C2×D3 | semidirect |
| 36. C2×C3×C42 | C3⋊D3 | semidirect |
| 48. C2×C33 | #126 | semidirect |
| 54. C3×C42 | C2×C3⋊D3 | semidirect |
| 66. C2×C42 | C3⋊(C3⋊D3) | semidirect |
| 67. C33 | C2×#126 | semidirect |
| 75. C2×C32 | #876 | semidirect |
| 83. C42 | C2×C3⋊(C3⋊D3) | semidirect |
| 90. C32 | C2×#876 | semidirect |
| 98. C2×C3 | #64085 | semidirect |
| 107. C3 | C2×#64085 | semidirect |
| 109. C2 | #11723917 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C42 | 2 |
| C2×#88859 | 2 |
| C2×#88857 | 2 |
| #11723917 | 2 |
| C2×#64085 | 3 |