Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
371 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#3745⋊C3 | C2 | semidirect |
| 2. C2×#88386 | C2 | semidirect |
| 3. #11720248 | C2 | direct (N × H) |
| 8. #3745⋊C3 | C22 | semidirect |
| 9. #88386 | C22 | semidirect |
| 10. C2×#3745 | D3 | semidirect |
| 28. #3745 | C2×D3 | semidirect |
| 59. C2×H(3,𝔽3) | D16 | semidirect |
| 90. H(3,𝔽3) | C2×D16 | semidirect |
| 111. C2×C32 | #826 | semidirect |
| 136. C32 | C2×#826 | semidirect |
| 161. C2 | #11720248 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745⋊C3 | 2 |
| C2×#88386 | 2 |
| #11720248 | 2 |
| C2×#63546 | 3 |