Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
476 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 130 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. C3×C9×#101 | C2 | semidirect |
| 4. C3×#63394 | C2 | semidirect |
| 5. C3×#63382 | C2 | semidirect |
| 7. D9×#101 | C3 | direct (N × H) |
| 27. C9×#101 | C2×C3 | semidirect |
| 28. #63394 | C2×C3 | semidirect |
| 29. #63382 | C2×C3 | semidirect |
| 85. C3×#101 | D9 | direct (N × H) |
| 125. C3×D9 | #101 | direct (N × H) |
| 173. #101 | C3×D9 | direct (N × H) |
| 174. C3×C9 | C2×#101 | semidirect |
| 216. D9 | C3×#101 | direct (N × H) |
| 249. C9 | C2×C3×#101 | semidirect |
| 283. C3 | D9×#101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×D9 | 2 |
| C3×M16×D9 | 2 |
| C3×C9×#101 | 2 |
| C3×#63394 | 2 |
| C3×#63382 | 2 |
| C3×D3×#101 | 3 |
| D9×#101 | 3 |