Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
594 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 137 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. #11721715 | C2 | semidirect |
| 4. #11720529 | C2 | semidirect |
| 5. C4⋊#6180 | C2 | semidirect |
| 23. D4×H(3,𝔽3) | Q8 | semidirect |
| 65. C32×D4 | Dic6 | semidirect |
| 112. H(3,𝔽3) | #474 | semidirect |
| 168. C32 | #5007 | semidirect |
| 172. D4 | #6229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×H(3,𝔽3) | 2 |
| #11721715 | 2 |
| #11720578 | 2 |
| #11720529 | 2 |
| C4⋊#6180 | 2 |
| C3×#5007 | 3 |