Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
935 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 935 conjugacy classes of subgroups — too many to draw. Only its 173 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×C42×H(3,𝔽3) | C2 | semidirect |
| 3. C2×#88538 | C2 | semidirect |
| 4. #11720522 | C2 | direct (N × H) |
| 11. #88740 | C4 | semidirect |
| 13. C2×C4⋊#272 | C4 | semidirect |
| 15. C2×#6229 | C4 | semidirect |
| 17. C42×H(3,𝔽3) | C22 | semidirect |
| 19. #88538 | C22 | semidirect |
| 22. C2×C32×C42 | D3 | semidirect |
| 39. C4⋊#272 | C2×C4 | semidirect |
| 43. #6229 | C2×C4 | semidirect |
| 58. C32×C42 | C2×D3 | semidirect |
| 105. C2×H(3,𝔽3) | #104 | semidirect |
| 152. C2×C42 | #272 | semidirect |
| 154. H(3,𝔽3) | C2×#104 | semidirect |
| 197. C2×C32 | #805 | semidirect |
| 214. C42 | C2×#272 | semidirect |
| 239. C32 | C2×#805 | semidirect |
| 287. C2 | #11720522 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88740 | 2 |
| C2×C42×H(3,𝔽3) | 2 |
| C2×#88538 | 2 |
| #11720522 | 2 |
| C2×C3×#805 | 3 |