Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1391 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1391 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×#634⋊C3 | C2 | semidirect |
| 3. C2×C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. C2×#88451 | C2 | semidirect |
| 5. #11721114 | C2 | direct (N × H) |
| 15. C2×#634⋊C3 | C22 | semidirect |
| 16. C4×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 17. #88451 | C22 | semidirect |
| 18. C22×#634 | D3 | semidirect |
| 23. C2×C4×C3⋊Dic3 | D3 | semidirect |
| 53. C2×#634 | C2×D3 | semidirect |
| 64. C4×C3⋊Dic3 | C2×D3 | semidirect |
| 125. C2×H(3,𝔽3) | #124 | semidirect |
| 193. H(3,𝔽3) | C2×#124 | semidirect |
| 240. C2×C32 | #875 | semidirect |
| 241. C2×C32 | #947 | semidirect |
| 294. C32 | C2×#875 | semidirect |
| 295. C32 | C2×#947 | semidirect |
| 338. C2 | #11721114 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#272 | 2 |
| C22×#634⋊C3 | 2 |
| C2×C4×(C3⋊Dic3)⋊C3 | 2 |
| C2×#88451 | 2 |
| #11721114 | 2 |
| C2×#63863 | 3 |
| C2×#63860 | 3 |