Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
476 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11720556 | C2 | semidirect |
| 5. C9×#824 | C2 | semidirect |
| 6. #11720299 | C2 | semidirect |
| 7. #11720290 | C2 | semidirect |
| 126. #824 | D9 | direct (N × H) |
| 179. C3×D9 | #101 | semidirect |
| 248. C3×C9 | C2×#101 | semidirect |
| 306. D9 | #824 | direct (N × H) |
| 350. C9 | C2×#824 | semidirect |
| 393. C3 | D9×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D9×Dic6 | 2 |
| C3×M16×D9 | 2 |
| D9×#208 | 2 |
| #11720556 | 2 |
| C9×#824 | 2 |
| #11720299 | 2 |
| #11720290 | 2 |
| D3×#824 | 3 |
| D9×#101 | 3 |