Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
532 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 2. C3×C9×#124 | C2 | semidirect |
| 3. C3×#63505 | C2 | semidirect |
| 4. C3×#63391 | C2 | semidirect |
| 5. C3×#63364 | C2 | semidirect |
| 7. #10588741 | C3 | direct (N × H) |
| 8. C2×C3×Q8×C9 | C22 | semidirect |
| 15. C3×C42×C9 | C22 | semidirect |
| 18. C3×#3667 | C22 | semidirect |
| 26. C9×#124 | C2×C3 | semidirect |
| 27. #63505 | C2×C3 | semidirect |
| 28. #63391 | C2×C3 | semidirect |
| 29. #63364 | C2×C3 | semidirect |
| 58. C2×Q8×C9 | C22×C3 | semidirect |
| 68. C42×C9 | C22×C3 | semidirect |
| 71. #3667 | C22×C3 | semidirect |
| 85. C3×#124 | D9 | semidirect |
| 134. C2×C3×Q8 | C2×D9 | semidirect |
| 152. C3×C42 | C2×D9 | semidirect |
| 183. #124 | C3×D9 | semidirect |
| 186. C3×C9 | #455 | semidirect |
| 234. C2×Q8 | C2×C3×D9 | semidirect |
| 242. C42 | C2×C3×D9 | semidirect |
| 269. C9 | C3×#455 | semidirect |
| 305. C3 | #10588741 | 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×#124 | 2 |
| C3×#63505 | 2 |
| C3×#63391 | 2 |
| C3×#63364 | 2 |
| C3×#5061 | 3 |
| #10588741 | 3 |