Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
812 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 395 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. #11722182 | C2 | semidirect |
| 56. C33 | #349 | semidirect |
| 78. C32 | #4553 | semidirect |
| 95. C3 | #10589419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| #11722182 | 2 |
| #10589419 | 3 |