Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
336 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 126 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×#108 | C2 | semidirect |
| 4. C3×#63381 | C2 | semidirect |
| 5. C3×#63372 | C2 | semidirect |
| 7. #10588573 | C3 | direct (N × H) |
| 24. C9×#108 | C2×C3 | semidirect |
| 25. #63381 | C2×C3 | semidirect |
| 26. #63372 | C2×C3 | semidirect |
| 69. C3×#108 | D9 | semidirect |
| 135. #108 | C3×D9 | semidirect |
| 136. C3×C9 | #430 | semidirect |
| 191. C9 | C3×#430 | semidirect |
| 216. C3 | #10588573 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×M16×D9 | 2 |
| C2×C3×#3663 | 2 |
| C3×C9×#108 | 2 |
| C3×#63381 | 2 |
| C3×#63372 | 2 |
| C3×#4893 | 3 |
| #10588573 | 3 |