Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
464 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 102 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×#63506 | C2 | semidirect |
| 3. C3×#63471 | C2 | semidirect |
| 4. C3×C9×#101 | C2 | semidirect |
| 5. C3×#63384 | C2 | semidirect |
| 7. #10588432 | C3 | direct (N × H) |
| 25. #63506 | C2×C3 | semidirect |
| 26. #63471 | C2×C3 | semidirect |
| 28. C9×#101 | C2×C3 | semidirect |
| 29. #63384 | C2×C3 | semidirect |
| 85. C3×#101 | D9 | semidirect |
| 169. #101 | C3×D9 | semidirect |
| 170. C3×C9 | #456 | semidirect |
| 241. C9 | C3×#456 | semidirect |
| 272. C3 | #10588432 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63713 | 2 |
| C3×#63506 | 2 |
| C3×#63471 | 2 |
| C3×C9×#101 | 2 |
| C3×#63384 | 2 |
| C3×#4752 | 3 |
| #10588432 | 3 |