Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
704 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#88528 | C2 | semidirect |
| 3. C4×#6229 | C2 | semidirect |
| 4. H(3,𝔽3)×C4⋊C8 | C2 | semidirect |
| 5. #11720554 | C2 | semidirect |
| 20. C32×C4⋊C8 | D3 | semidirect |
| 33. #6229 | D4 | semidirect |
| 52. C4×H(3,𝔽3) | SD16 | semidirect |
| 110. C32×C4 | #204 | semidirect |
| 118. C4⋊C8 | #272 | semidirect |
| 120. H(3,𝔽3) | #460 | semidirect |
| 181. C32 | #4848 | semidirect |
| 210. C4 | #88528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88528 | 2 |
| #11721720 | 2 |
| C4×#6229 | 2 |
| H(3,𝔽3)×C4⋊C8 | 2 |
| #11720554 | 2 |
| C3×#4848 | 3 |