Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#88547 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. #11720527 | C2 | semidirect |
| 7. #11720526 | C2 | semidirect |
| 195. C3×C9 | #470 | semidirect |
| 270. C9 | #5052 | semidirect |
| 305. C3 | #10588728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C22⋊Q8 | 2 |
| C2×#88547 | 2 |
| #11721813 | 2 |
| C2×#88532 | 2 |
| #11720582 | 2 |
| #11720527 | 2 |
| #11720526 | 2 |
| #10592751 | 3 |
| #10588728 | 3 |