Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1699 conjugacy classes of subgroups; only the 499 normal subgroups are shown.
This group has 1699 conjugacy classes of subgroups — too many to draw. Only its 499 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 |
|---|---|---|
| 4. C2×#88448 | C2 | direct (N × H) |
| 11. C22×(C3⋊Dic3)⋊C3 | C4 | semidirect |
| 14. #88448 | C22 | direct (N × H) |
| 31. C2×(C3⋊Dic3)⋊C3 | C2×C4 | semidirect |
| 41. C22×C3⋊Dic3 | Dic3 | semidirect |
| 56. C22×H(3,𝔽3) | C4⋊C4 | semidirect |
| 63. (C3⋊Dic3)⋊C3 | C22×C4 | semidirect |
| 90. C2×C3⋊Dic3 | C2×Dic3 | semidirect |
| 104. C2×H(3,𝔽3) | C2×C4⋊C4 | semidirect |
| 140. C22×C32 | Dic3⋊C4 | semidirect |
| 141. C22×C32 | C4⋊Dic3 | semidirect |
| 151. C3⋊Dic3 | C22×Dic3 | semidirect |
| 161. H(3,𝔽3) | C22×C4⋊C4 | semidirect |
| 202. C2×C32 | C2×Dic3⋊C4 | semidirect |
| 203. C2×C32 | C2×C4⋊Dic3 | semidirect |
| 249. C32 | C22×Dic3⋊C4 | semidirect |
| 250. C32 | C22×C4⋊Dic3 | semidirect |
| 277. C22 | #88448 | direct (N × H) |
| 289. C2 | C2×#88448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1084 | 2 |
| C23×(C3⋊Dic3)⋊C3 | 2 |
| C2×#88448 | 2 |
| C22×#3724 | 3 |
| C22×Dic3⋊Dic3 | 3 |