Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1012 conjugacy classes of subgroups; only the 304 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 304 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 |
|---|---|---|
| 3. #11722173 | C2 | semidirect |
| 4. C3×#63630 | C2 | semidirect |
| 5. Dic3×C3⋊(C3⋊C8) | C2 | semidirect |
| 15. #88786 | C4 | semidirect |
| 23. #63630 | D3 | semidirect |
| 34. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 35. C3×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 62. C32×Dic3 | M16 | semidirect |
| 93. C3⋊(C3⋊C8) | C4×D3 | semidirect |
| 132. C3×Dic3 | #208 | semidirect |
| 139. C33 | C4×M16 | semidirect |
| 192. Dic3 | #3748 | semidirect |
| 195. C32 | #4707 | semidirect |
| 196. C32 | C4×#208 | semidirect |
| 222. C3 | #10590334 | semidirect |
| 223. C3 | C4×#3748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C42×D3 | 2 |
| C2×#88786 | 2 |
| #11722173 | 2 |
| C3×#63630 | 2 |
| Dic3×C3⋊(C3⋊C8) | 2 |
| C4×#3748 | 3 |
| #10590334 | 3 |