Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
429 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #11720783 | C2 | semidirect |
| 4. C4×#6188 | C2 | semidirect |
| 8. #88631 | C4 | direct (N × H) |
| 25. #6188 | C2×C4 | semidirect |
| 39. C4×H(3,𝔽3) | M16 | semidirect |
| 42. #1084 | M16 | semidirect |
| 94. H(3,𝔽3) | C4×M16 | semidirect |
| 178. C4 | #88631 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88631 | 2 |
| C2×C4×#1084 | 2 |
| #11720783 | 2 |
| C4×#6188 | 2 |
| C3×C4×M16 | 9 |