Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1428 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 1428 conjugacy classes of subgroups — too many to draw. Only its 579 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 |
|---|---|---|
| 4. #11722192 | C2 | semidirect |
| 90. C33 | #430 | semidirect |
| 123. C32 | #5124 | semidirect |
| 146. C3 | #10592823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| C2×#88855 | 2 |
| #11722192 | 2 |
| #10592823 | 3 |