Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
940 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 174 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. #11724517 | C2 | semidirect |
| 3. C3×#64289 | C2 | semidirect |
| 4. #11724253 | C2 | semidirect |
| 5. #11724252 | C2 | semidirect |
| 6. D3×#3788 | C2 | semidirect |
| 7. D3×#3787 | C2 | semidirect |
| 16. #88989 | C22 | semidirect |
| 17. #88988 | C22 | semidirect |
| 18. C3×#3788 | C22 | semidirect |
| 19. C3×#3787 | C22 | semidirect |
| 20. #88926 | C22 | semidirect |
| 21. #88924 | C22 | semidirect |
| 22. #88924 | C22 | semidirect |
| 30. #64289 | D3 | direct (N × H) |
| 69. #3788 | C2×D3 | semidirect |
| 73. #3787 | C2×D3 | semidirect |
| 125. C32×D3 | #131 | semidirect |
| 176. C33 | C2×#131 | semidirect |
| 255. C32 | D3×#131 | semidirect |
| 281. D3 | #64289 | direct (N × H) |
| 292. C3 | C2×#64289 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#3832 | 2 |
| #11724517 | 2 |
| C3×#64289 | 2 |
| #11724253 | 2 |
| #11724252 | 2 |
| D3×#3788 | 2 |
| D3×#3787 | 2 |
| C2×#64289 | 3 |
| D3×#131 | 9 |