Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1484 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 1484 conjugacy classes of subgroups — too many to draw. Only its 411 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. C33×#131 | C2 | semidirect |
| 3. #11723942 | C2 | semidirect |
| 4. #11722207 | C2 | semidirect |
| 5. #11722195 | C2 | semidirect |
| 6. #11722192 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 15. #88863 | C4 | semidirect |
| 16. #88862 | C4 | semidirect |
| 17. #88861 | C4 | semidirect |
| 18. #88860 | C4 | semidirect |
| 24. C32×#131 | D3 | semidirect |
| 71. C3×#131 | C3⋊D3 | semidirect |
| 124. #131 | C3⋊(C3⋊D3) | semidirect |
| 129. C33 | #443 | semidirect |
| 173. C32 | #5144 | semidirect |
| 202. C3 | #10592843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#131 | 2 |
| #11723991 | 2 |
| #11723942 | 2 |
| #11722207 | 2 |
| #11722195 | 2 |
| #11722192 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #10592843 | 3 |