Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
372 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 87 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×C3×#3674 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. #11720268 | C2 | semidirect |
| 7. #11720264 | C2 | semidirect |
| 31. C2×#3674 | D3 | semidirect |
| 214. C3×C9 | #470 | semidirect |
| 304. C9 | #5189 | semidirect |
| 343. C3 | #10588728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#946 | 2 |
| C2×C3×#3674 | 2 |
| #11720960 | 2 |
| C2×#88420 | 2 |
| #11720582 | 2 |
| #11720268 | 2 |
| #11720264 | 2 |
| #10591638 | 3 |
| #10588728 | 3 |