Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1298 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1298 conjugacy classes of subgroups — too many to draw. Only its 219 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. #11721846 | C2 | semidirect |
| 3. #11721845 | C2 | semidirect |
| 4. D4×#1084 | C2 | semidirect |
| 5. C4×#6229 | C2 | semidirect |
| 105. H(3,𝔽3) | #559 | semidirect |
| 151. C32 | #5713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#127 | 2 |
| #11721846 | 2 |
| #11721845 | 2 |
| D4×#1084 | 2 |
| C4×#6229 | 2 |
| C3×#5713 | 3 |