Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
770 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 770 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×#88529 | C2 | semidirect |
| 2. #11721720 | C2 | semidirect |
| 3. C4×C4⋊#272 | C2 | semidirect |
| 4. H(3,𝔽3)×C4⋊C8 | C2 | semidirect |
| 5. #11720554 | C2 | semidirect |
| 20. C32×C4⋊C8 | D3 | semidirect |
| 33. C4⋊#272 | D4 | semidirect |
| 56. C4×H(3,𝔽3) | D8 | semidirect |
| 118. C32×C4 | D24 | semidirect |
| 125. C4⋊C8 | #272 | semidirect |
| 127. H(3,𝔽3) | #459 | semidirect |
| 195. C32 | #4843 | semidirect |
| 229. C4 | #88529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88529 | 2 |
| #11721720 | 2 |
| C4×C4⋊#272 | 2 |
| H(3,𝔽3)×C4⋊C8 | 2 |
| #11720554 | 2 |
| C3×#4843 | 3 |