Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1419 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 281 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. C2×#88552 | C2 | semidirect |
| 3. C2×C4⋊#1084 | C2 | semidirect |
| 4. C2×C4×#1084 | C2 | semidirect |
| 9. C2×D4×H(3,𝔽3) | C4 | semidirect |
| 34. C2×#1084 | D4 | semidirect |
| 40. C2×C32×D4 | Dic3 | semidirect |
| 57. C4×H(3,𝔽3) | C22⋊C4 | semidirect |
| 120. C32×C4 | #217 | semidirect |
| 127. H(3,𝔽3) | #390 | semidirect |
| 167. C2×D4 | #1084 | semidirect |
| 200. C32 | #5221 | semidirect |
| 240. C4 | #88552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×H(3,𝔽3) | 2 |
| C2×#88552 | 2 |
| C2×C4⋊#1084 | 2 |
| C2×C4×#1084 | 2 |
| C3×#5221 | 3 |