Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
612 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 612 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 |
|---|---|---|
| 1. C3×#63710 | C2 | semidirect |
| 2. C3×C9×#127 | C2 | semidirect |
| 3. C3×#63495 | C2 | semidirect |
| 4. C3×#63391 | C2 | semidirect |
| 5. C3×#63364 | C2 | semidirect |
| 7. #10588757 | C3 | direct (N × H) |
| 10. C2×C3×D4×C9 | C22 | semidirect |
| 15. C3×C42×C9 | C22 | semidirect |
| 18. C3×#3667 | C22 | semidirect |
| 22. #63710 | C2×C3 | semidirect |
| 26. C9×#127 | C2×C3 | semidirect |
| 27. #63495 | C2×C3 | semidirect |
| 28. #63391 | C2×C3 | semidirect |
| 29. #63364 | C2×C3 | semidirect |
| 41. C3×D36 | D4 | semidirect |
| 43. C3×Dic18 | D4 | semidirect |
| 63. C2×D4×C9 | C22×C3 | semidirect |
| 69. C42×C9 | C22×C3 | semidirect |
| 72. #3667 | C22×C3 | semidirect |
| 87. C3×#127 | D9 | semidirect |
| 127. D36 | C3×D4 | semidirect |
| 129. Dic18 | C3×D4 | semidirect |
| 147. C2×C3×D4 | C2×D9 | semidirect |
| 158. C3×C42 | C2×D9 | semidirect |
| 192. #127 | C3×D9 | semidirect |
| 195. C3×C9 | #453 | semidirect |
| 253. C2×D4 | C2×C3×D9 | semidirect |
| 257. C42 | C2×C3×D9 | semidirect |
| 287. C9 | C3×#453 | semidirect |
| 328. C3 | #10588757 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63710 | 2 |
| C3×C9×#127 | 2 |
| C3×#63495 | 2 |
| C3×#63391 | 2 |
| C3×#63364 | 2 |
| C3×#5077 | 3 |
| #10588757 | 3 |