Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1180 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1180 conjugacy classes of subgroups — too many to draw. Only its 234 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×#1007 | C2 | semidirect |
| 2. C33×#124 | C2 | semidirect |
| 3. C32×#932 | C2 | semidirect |
| 4. C32×#836 | C2 | semidirect |
| 5. C32×#805 | C2 | semidirect |
| 7. C3×#5062 | C3 | direct (N × H) |
| 20. C3×#1007 | C2×C3 | semidirect |
| 23. C32×#124 | D3 | semidirect |
| 24. C32×#124 | C2×C3 | semidirect |
| 25. C3×#932 | C2×C3 | semidirect |
| 28. C3×#836 | C2×C3 | semidirect |
| 29. C3×#805 | C2×C3 | semidirect |
| 45. #5062 | C32 | direct (N × H) |
| 81. #1007 | C2×C32 | semidirect |
| 84. C3×#124 | C3×D3 | semidirect |
| 85. C3×#124 | C2×C32 | semidirect |
| 86. #932 | C2×C32 | semidirect |
| 89. #836 | C2×C32 | semidirect |
| 90. #805 | C2×C32 | semidirect |
| 180. #124 | C32×D3 | semidirect |
| 183. C33 | #454 | semidirect |
| 263. C32 | #5062 | direct (N × H) |
| 264. C32 | C3×#454 | semidirect |
| 299. C3 | C3×#5062 | direct (N × H) |
| 300. C3 | C32×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1007 | 2 |
| C33×#124 | 2 |
| C32×#932 | 2 |
| C32×#836 | 2 |
| C32×#805 | 2 |
| C32×#454 | 3 |
| C3×#5062 | 3 |