Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1456 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 1456 conjugacy classes of subgroups — too many to draw. Only its 357 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. #11723948 | C2 | semidirect |
| 3. C33×#108 | C2 | semidirect |
| 4. #11722195 | C2 | semidirect |
| 5. #11722185 | C2 | semidirect |
| 12. #88853 | C4 | semidirect |
| 13. #88852 | C4 | semidirect |
| 14. #88851 | C4 | semidirect |
| 19. C32×#108 | D3 | semidirect |
| 51. C3×#108 | C3⋊D3 | semidirect |
| 86. #108 | C3⋊(C3⋊D3) | semidirect |
| 89. C33 | #444 | semidirect |
| 119. C32 | #4894 | semidirect |
| 139. C3 | #10592593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723948 | 2 |
| #11723945 | 2 |
| C33×#108 | 2 |
| #11722195 | 2 |
| #11722185 | 2 |
| #10592593 | 3 |