Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2935 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 2935 conjugacy classes of subgroups — too many to draw. Only its 555 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. C22×#6229 | C2 | semidirect |
| 2. C2×#3828⋊C3 | C2 | semidirect |
| 3. C2×#88672 | C2 | semidirect |
| 4. #11722483 | C2 | direct (N × H) |
| 5. C2×#88648 | C2 | semidirect |
| 6. C2×((C3⋊D3)⋊C3)⋊Q8 | C2 | semidirect |
| 11. C2×#6229 | C22 | semidirect |
| 13. #3828⋊C3 | C22 | semidirect |
| 18. #88672 | C22 | semidirect |
| 21. #88648 | C22 | semidirect |
| 22. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 23. C2×#3828 | D3 | semidirect |
| 53. #3828 | C2×D3 | semidirect |
| 134. C2×H(3,𝔽3) | 2−1+4 | semidirect |
| 203. H(3,𝔽3) | C2×2−1+4 | semidirect |
| 253. C2×C32 | #1010 | semidirect |
| 298. C32 | C2×#1010 | semidirect |
| 339. C2 | #11722483 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6229 | 2 |
| C2×#3828⋊C3 | 2 |
| C2×#88672 | 2 |
| #11722483 | 2 |
| C2×#88648 | 2 |
| C2×((C3⋊D3)⋊C3)⋊Q8 | 2 |
| C2×#64297 | 3 |