Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
808 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 230 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 |
|---|---|---|
| 6. #10592415 | C3 | direct (N × H) |
| 15. C3×#3746 | C4 | semidirect |
| 51. #3746 | C3×C4 | semidirect |
| 136. C33 | #441 | semidirect |
| 188. C32 | #4716 | semidirect |
| 189. C32 | C3×#441 | semidirect |
| 211. C3 | C3×#4716 | semidirect |
| 212. C3 | #10592415 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3746 | 2 |
| C3×C4×#634 | 2 |
| C33×#97 | 2 |
| C3×#63644 | 2 |
| C3×#63643 | 2 |
| #10592415 | 3 |
| C3×#4716 | 3 |