Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1300 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 1300 conjugacy classes of subgroups — too many to draw. Only its 248 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. D3×#3748 | C2 | semidirect |
| 3. #11722203 | C2 | semidirect |
| 4. C3×#63660 | C2 | semidirect |
| 5. #11722025 | C2 | semidirect |
| 15. #88855 | C22 | semidirect |
| 16. C3×#3748 | C22 | semidirect |
| 27. #63660 | D3 | direct (N × H) |
| 66. #3748 | C2×D3 | semidirect |
| 134. C32×D3 | #100 | semidirect |
| 192. C33 | C2×#100 | semidirect |
| 241. C3×D3 | #833 | semidirect |
| 282. C32 | D3×#100 | semidirect |
| 283. C32 | C2×#833 | semidirect |
| 313. D3 | #63660 | direct (N × H) |
| 327. C3 | D3×#833 | semidirect |
| 328. C3 | C2×#63660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D3×D4 | 2 |
| D3×#3748 | 2 |
| #11722203 | 2 |
| C3×#63660 | 2 |
| #11722025 | 2 |
| C2×#63660 | 3 |
| D3×#833 | 3 |