Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1111 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1111 conjugacy classes of subgroups — too many to draw. Only its 277 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×C4⋊#1084 | C2 | semidirect |
| 3. C22×#6180 | C2 | semidirect |
| 4. #11720578 | C2 | direct (N × H) |
| 9. C2×D4×H(3,𝔽3) | C4 | semidirect |
| 14. C4⋊#1084 | C22 | semidirect |
| 16. C2×#6180 | C22 | semidirect |
| 28. D4×H(3,𝔽3) | C2×C4 | semidirect |
| 41. C2×C32×D4 | Dic3 | semidirect |
| 76. C32×D4 | C2×Dic3 | semidirect |
| 86. C2×H(3,𝔽3) | #102 | semidirect |
| 128. H(3,𝔽3) | C2×#102 | semidirect |
| 160. C2×C32 | #832 | semidirect |
| 167. C2×D4 | #1084 | semidirect |
| 199. C32 | C2×#832 | semidirect |
| 207. D4 | C2×#1084 | semidirect |
| 240. C2 | #11720578 | direct (N × H) |
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×C4⋊#1084 | 2 |
| C22×#6180 | 2 |
| #11720578 | 2 |
| C2×C3×#832 | 3 |