Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
350 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C3×#63505 | C2 | semidirect |
| 2. C2×C3×#3675 | C2 | semidirect |
| 4. C3×#63469 | C2 | semidirect |
| 5. C3×C9×#101 | C2 | semidirect |
| 6. C3×#63383 | C2 | semidirect |
| 7. C3×#63381 | C2 | semidirect |
| 9. #10588434 | C3 | direct (N × H) |
| 32. #63505 | C2×C3 | semidirect |
| 33. C2×#3675 | C2×C3 | semidirect |
| 35. #63469 | C2×C3 | semidirect |
| 37. C9×#101 | C2×C3 | semidirect |
| 38. #63383 | C2×C3 | semidirect |
| 39. #63381 | C2×C3 | semidirect |
| 109. C3×#101 | D9 | semidirect |
| 215. #101 | C3×D9 | semidirect |
| 217. C3×C9 | #471 | semidirect |
| 303. C9 | C3×#471 | semidirect |
| 339. C3 | #10588434 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63505 | 2 |
| C2×C3×#3675 | 2 |
| C3×#63470 | 2 |
| C3×#63469 | 2 |
| C3×C9×#101 | 2 |
| C3×#63383 | 2 |
| C3×#63381 | 2 |
| C3×#4754 | 3 |
| #10588434 | 3 |