Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
495 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11720574 | C2 | semidirect |
| 3. #11720573 | C2 | semidirect |
| 6. C2×D4×H(3,𝔽3) | C4 | semidirect |
| 9. C4⋊C4×H(3,𝔽3) | C4 | semidirect |
| 31. C2×C32×D4 | Dic3 | semidirect |
| 34. C32×C4⋊C4 | Dic3 | semidirect |
| 104. H(3,𝔽3) | #327 | semidirect |
| 138. C2×D4 | #1084 | semidirect |
| 142. C4⋊C4 | #1084 | semidirect |
| 168. C32 | #4537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#121 | 2 |
| #11720574 | 2 |
| #11720573 | 2 |
| C3×#4537 | 3 |