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 |
|---|---|---|
| 3. C2×#88428 | C2 | semidirect |
| 5. #11720527 | C2 | semidirect |
| 6. C3×#63367 | C2 | semidirect |
| 7. #11720297 | C2 | semidirect |
| 37. #63367 | D3 | semidirect |
| 214. C3×C9 | #470 | semidirect |
| 304. C9 | #4867 | 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×#897 | 2 |
| #11720961 | 2 |
| C2×#88428 | 2 |
| C2×#88420 | 2 |
| #11720527 | 2 |
| C3×#63367 | 2 |
| #11720297 | 2 |
| #10590587 | 3 |
| #10588728 | 3 |