Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
368 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 368 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×#63454 | C2 | semidirect |
| 3. C3×C9×#102 | C2 | semidirect |
| 4. C3×#63392 | C2 | semidirect |
| 5. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 6. C3×#63377 | C2 | semidirect |
| 7. C3×#63366 | C2 | semidirect |
| 9. #10588459 | C3 | direct (N × H) |
| 29. #63454 | C2×C3 | semidirect |
| 31. C9×#102 | C2×C3 | semidirect |
| 32. #63392 | C2×C3 | semidirect |
| 33. (C2×D9)⋊C8 | C2×C3 | semidirect |
| 34. #63377 | C2×C3 | semidirect |
| 35. #63366 | C2×C3 | semidirect |
| 98. C3×#102 | D9 | semidirect |
| 208. #102 | C3×D9 | semidirect |
| 210. C3×C9 | #482 | semidirect |
| 305. C9 | C3×#482 | semidirect |
| 348. C3 | #10588459 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63500 | 2 |
| C3×#63454 | 2 |
| C3×C9×#102 | 2 |
| C3×#63392 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| C3×#63377 | 2 |
| C3×#63366 | 2 |
| C3×#4779 | 3 |
| #10588459 | 3 |