Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
560 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#88521 | C2 | semidirect |
| 4. #11721743 | C2 | semidirect |
| 6. #11720537 | C2 | semidirect |
| 7. #11720527 | C2 | semidirect |
| 195. C3×C9 | #464 | semidirect |
| 270. C9 | #4767 | semidirect |
| 305. C3 | #10588447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721836 | 2 |
| C2×#88543 | 2 |
| C2×#88521 | 2 |
| #11721743 | 2 |
| C3×C9×#102 | 2 |
| #11720537 | 2 |
| #11720527 | 2 |
| #10592466 | 3 |
| #10588447 | 3 |