Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
737 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 737 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4×D4×H(3,𝔽3) | C2 | semidirect |
| 3. C4×C4⋊#272 | C2 | semidirect |
| 4. #11720578 | C2 | semidirect |
| 5. #11720531 | C2 | semidirect |
| 6. #11720529 | C2 | semidirect |
| 7. C4×#6180 | C2 | semidirect |
| 16. #88545 | C4 | direct (N × H) |
| 21. C32×C4×D4 | D3 | semidirect |
| 31. D4×H(3,𝔽3) | C2×C4 | semidirect |
| 39. C4⋊#272 | C2×C4 | semidirect |
| 42. #6180 | C2×C4 | semidirect |
| 66. C4×H(3,𝔽3) | D8 | semidirect |
| 87. C32×D4 | C4×D3 | semidirect |
| 138. C32×C4 | #213 | semidirect |
| 144. C4×D4 | #272 | semidirect |
| 149. H(3,𝔽3) | C4×D8 | semidirect |
| 223. C32 | C4×#213 | semidirect |
| 229. D4 | C4×#272 | semidirect |
| 259. C4 | #88545 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×H(3,𝔽3) | 2 |
| C2×#88545 | 2 |
| C4×C4⋊#272 | 2 |
| #11720578 | 2 |
| #11720531 | 2 |
| #11720529 | 2 |
| C4×#6180 | 2 |
| C3×C4×#213 | 3 |