Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
340 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 340 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×#63431 | C2 | semidirect |
| 3. C3×C9×#97 | C2 | semidirect |
| 5. C3×#63376 | C2 | semidirect |
| 7. #10588395 | C3 | direct (N × H) |
| 23. #63431 | C2×C3 | semidirect |
| 25. C9×#97 | C2×C3 | semidirect |
| 27. #63376 | C2×C3 | semidirect |
| 76. C3×#97 | D9 | semidirect |
| 155. #97 | C3×D9 | semidirect |
| 156. C3×C9 | #489 | semidirect |
| 225. C9 | C3×#489 | semidirect |
| 257. C3 | #10588395 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63437 | 2 |
| C3×#63431 | 2 |
| C3×C9×#97 | 2 |
| C3×#63380 | 2 |
| C3×#63376 | 2 |
| C3×#4714 | 3 |
| #10588395 | 3 |