Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
561 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 561 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 25. #6229 | C8 | direct (N × H) |
| 27. C8×H(3,𝔽3) | Q8 | semidirect |
| 63. C32×C8 | Dic6 | semidirect |
| 97. H(3,𝔽3) | C8×Q8 | semidirect |
| 141. C32 | C8×Dic6 | semidirect |
| 150. C8 | #6229 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6229 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #11720547 | 2 |
| C8×#1084 | 2 |
| C4⋊#6180 | 2 |
| C3×C8×Dic6 | 3 |