Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1680 conjugacy classes of subgroups; only the 467 normal subgroups are shown.
This group has 1680 conjugacy classes of subgroups — too many to draw. Only its 467 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 |
|---|---|---|
| 3. C4×#6308 | C2 | semidirect |
| 5. #11722180 | C2 | semidirect |
| 6. #11722177 | C2 | semidirect |
| 7. #11722173 | C2 | semidirect |
| 15. #88861 | C4 | semidirect |
| 39. #6308 | C2×C4 | semidirect |
| 41. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 122. C33 | #440 | semidirect |
| 164. C32 | #5018 | semidirect |
| 194. C3 | #10592717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×D4 | 2 |
| C2×#88861 | 2 |
| C4×#6308 | 2 |
| #11722202 | 2 |
| #11722180 | 2 |
| #11722177 | 2 |
| #11722173 | 2 |
| #10592717 | 3 |