Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
495 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11721779 | C2 | semidirect |
| 2. C2×#88529 | C2 | semidirect |
| 3. H(3,𝔽3)×M32 | C2 | semidirect |
| 4. #11720513 | C2 | semidirect |
| 5. #11720512 | C2 | semidirect |
| 10. #88530 | C22 | semidirect |
| 13. #88529 | C22 | semidirect |
| 15. C16×H(3,𝔽3) | C22 | semidirect |
| 18. C32×M32 | D3 | semidirect |
| 41. C32×C16 | C2×D3 | semidirect |
| 103. M32 | #272 | semidirect |
| 104. H(3,𝔽3) | #509 | semidirect |
| 137. C16 | C2×#272 | semidirect |
| 152. C32 | #4908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721779 | 2 |
| C2×#88529 | 2 |
| H(3,𝔽3)×M32 | 2 |
| #11720513 | 2 |
| #11720512 | 2 |
| C3×#4908 | 3 |