Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #11720924 | C2 | semidirect |
| 5. C2×#88427 | C2 | semidirect |
| 6. C2×#88418 | C2 | semidirect |
| 7. #11720274 | C2 | semidirect |
| 215. C3×C9 | #497 | semidirect |
| 304. C9 | #5060 | semidirect |
| 340. C3 | #10588847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88543 | 2 |
| C3×#63498 | 2 |
| C2×C9×#214 | 2 |
| #11720924 | 2 |
| C2×#88427 | 2 |
| C2×#88418 | 2 |
| #11720274 | 2 |
| #10591491 | 3 |
| #10588847 | 3 |