Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
342 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 1. C3×#63471 | C2 | semidirect |
| 3. C2×C3×#3664 | C2 | semidirect |
| 4. C3×#63464 | C2 | semidirect |
| 5. C3×C9×#108 | C2 | semidirect |
| 6. C3×#63383 | C2 | semidirect |
| 7. C3×#63382 | C2 | semidirect |
| 9. #10588578 | C3 | direct (N × H) |
| 32. #63471 | C2×C3 | semidirect |
| 34. C2×#3664 | C2×C3 | semidirect |
| 35. #63464 | C2×C3 | semidirect |
| 37. C9×#108 | C2×C3 | semidirect |
| 38. #63383 | C2×C3 | semidirect |
| 39. #63382 | C2×C3 | semidirect |
| 108. C3×#108 | D9 | semidirect |
| 212. #108 | C3×D9 | semidirect |
| 215. C3×C9 | #471 | semidirect |
| 299. C9 | C3×#471 | semidirect |
| 335. C3 | #10588578 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63471 | 2 |
| C3×#63470 | 2 |
| C2×C3×#3664 | 2 |
| C3×#63464 | 2 |
| C3×C9×#108 | 2 |
| C3×#63383 | 2 |
| C3×#63382 | 2 |
| C3×#4898 | 3 |
| #10588578 | 3 |