Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
342 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 98 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×#63450 | C2 | semidirect |
| 3. C3×C9×#103 | C2 | semidirect |
| 4. C3×#63395 | C2 | semidirect |
| 6. C3×#63375 | C2 | semidirect |
| 9. #10588474 | C3 | direct (N × H) |
| 29. #63450 | C2×C3 | semidirect |
| 31. C9×#103 | C2×C3 | semidirect |
| 32. #63395 | C2×C3 | semidirect |
| 34. #63375 | C2×C3 | semidirect |
| 94. C3×#103 | D9 | semidirect |
| 197. #103 | C3×D9 | semidirect |
| 201. C3×C9 | #489 | semidirect |
| 287. C9 | C3×#489 | semidirect |
| 325. C3 | #10588474 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63509 | 2 |
| C3×#63450 | 2 |
| C3×C9×#103 | 2 |
| C3×#63395 | 2 |
| C3×#63380 | 2 |
| C3×#63375 | 2 |
| C3×#63369 | 2 |
| C3×#4794 | 3 |
| #10588474 | 3 |