Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1048 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 258 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. C2×C32×#216 | C2 | semidirect |
| 4. C32×#869 | C2 | semidirect |
| 5. C32×#803 | C2 | semidirect |
| 7. C3×#5060 | C3 | direct (N × H) |
| 23. C2×C3×#216 | C2×C3 | semidirect |
| 25. C3×#869 | C2×C3 | semidirect |
| 27. C3×#803 | C2×C3 | semidirect |
| 39. #5060 | C32 | direct (N × H) |
| 75. C2×#216 | C2×C32 | semidirect |
| 77. #869 | C2×C32 | semidirect |
| 79. #803 | C2×C32 | semidirect |
| 157. C33 | #497 | semidirect |
| 223. C32 | #5060 | direct (N × H) |
| 224. C32 | C3×#497 | semidirect |
| 252. C3 | C3×#5060 | direct (N × H) |
| 253. C3 | C32×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#124 | 2 |
| C2×C32×#216 | 2 |
| C2×C32×#214 | 2 |
| C32×#869 | 2 |
| C32×#803 | 2 |
| C32×#497 | 3 |
| C3×#5060 | 3 |