Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1004 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 186 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. #11723484 | C2 | semidirect |
| 2. Dic3×C4⋊(C3⋊D3) | C2 | semidirect |
| 4. #11722191 | C2 | semidirect |
| 5. C3×#63648 | C2 | semidirect |
| 6. C32×C8×Dic3 | C2 | semidirect |
| 7. #11722055 | C2 | semidirect |
| 21. #88791 | C4 | semidirect |
| 32. #63648 | D3 | semidirect |
| 35. C3×C8×Dic3 | D3 | semidirect |
| 42. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 45. C3×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 51. C32×C3⋊C8 | C2×C4 | semidirect |
| 93. C32×Dic3 | D8 | semidirect |
| 107. C8×Dic3 | C3⋊D3 | semidirect |
| 130. C4⋊(C3⋊D3) | C4×D3 | semidirect |
| 144. C3×C3⋊C8 | C4×D3 | semidirect |
| 210. C3×Dic3 | D24 | semidirect |
| 218. C33 | C4×D8 | semidirect |
| 254. C3⋊C8 | C4×C3⋊D3 | semidirect |
| 313. Dic3 | #3745 | semidirect |
| 315. C32 | C4×D24 | semidirect |
| 316. C32 | #4756 | semidirect |
| 360. C3 | #10590745 | semidirect |
| 361. C3 | C4×#3745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723484 | 2 |
| Dic3×C4⋊(C3⋊D3) | 2 |
| C2×#88791 | 2 |
| #11722191 | 2 |
| C3×#63648 | 2 |
| C32×C8×Dic3 | 2 |
| #11722055 | 2 |
| C4×#3745 | 3 |
| #10590745 | 3 |