Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1540 conjugacy classes of subgroups; only the 415 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 415 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 |
|---|---|---|
| 14. #88853 | C4 | semidirect |
| 44. C3⋊(C3⋊Dic3) | Q16 | semidirect |
| 83. C33 | C4×Q16 | semidirect |
| 111. C32 | #4873 | semidirect |
| 131. C3 | #10592572 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88853 | 2 |
| #11723928 | 2 |
| C33×#107 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #11722180 | 2 |
| #10592572 | 3 |