Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
349 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 65 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. C2×#3746⋊C3 | C2 | semidirect |
| 3. #63639⋊C3 | C2 | semidirect |
| 4. #11720256 | C2 | semidirect |
| 5. #11720254 | C2 | semidirect |
| 17. C2×#3746 | D3 | semidirect |
| 22. #63639 | D3 | semidirect |
| 171. H(3,𝔽3) | #510 | semidirect |
| 251. C32 | #4909 | semidirect |
| 252. C32 | #5179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721779 | 2 |
| C2×#3746⋊C3 | 2 |
| #63639⋊C3 | 2 |
| #11720256 | 2 |
| #11720254 | 2 |
| #10590638 | 3 |
| #10590636 | 3 |