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 |
|---|---|---|
| 2. C4×C4⋊#272 | C2 | semidirect |
| 3. C4×C8×H(3,𝔽3) | C2 | semidirect |
| 4. #11720554 | C2 | semidirect |
| 5. #11720551 | C2 | semidirect |
| 14. #88529 | C4 | direct (N × H) |
| 17. C32×C4×C8 | D3 | semidirect |
| 26. C4⋊#272 | C2×C4 | semidirect |
| 29. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 45. C4×H(3,𝔽3) | D8 | semidirect |
| 68. C32×C8 | C4×D3 | semidirect |
| 95. C32×C4 | D24 | semidirect |
| 103. C4×C8 | #272 | semidirect |
| 104. H(3,𝔽3) | C4×D8 | semidirect |
| 155. C32 | C4×D24 | semidirect |
| 165. C8 | C4×#272 | semidirect |
| 180. C4 | #88529 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88529 | 2 |
| C4×C4⋊#272 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #11720554 | 2 |
| #11720551 | 2 |
| C3×C4×D24 | 3 |