Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
370 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×#63432 | C2 | semidirect |
| 3. C3×C9×#97 | C2 | semidirect |
| 4. C3×#63380 | C2 | semidirect |
| 6. #10588394 | C3 | direct (N × H) |
| 18. #63432 | C2×C3 | semidirect |
| 20. C9×#97 | C2×C3 | semidirect |
| 21. #63380 | C2×C3 | semidirect |
| 57. C3×#97 | D9 | semidirect |
| 113. #97 | C3×D9 | semidirect |
| 114. C3×C9 | #490 | semidirect |
| 163. C9 | C3×#490 | semidirect |
| 186. C3 | #10588394 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63436 | 2 |
| C3×#63432 | 2 |
| C3×C9×#97 | 2 |
| C3×#63380 | 2 |
| C3×#4713 | 3 |
| #10588394 | 3 |