Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
971 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 971 conjugacy classes of subgroups — too many to draw. Only its 147 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×#88651 | C2 | semidirect |
| 3. C2×#88527 | C2 | semidirect |
| 4. C2×#3744⋊C3 | C2 | semidirect |
| 5. C2×#3746⋊C3 | C2 | semidirect |
| 6. C2×#88433 | C2 | semidirect |
| 7. C2×#88431 | C2 | semidirect |
| 8. #11720845 | C2 | direct (N × H) |
| 21. #88651 | C22 | semidirect |
| 26. #88527 | C22 | semidirect |
| 27. #3744⋊C3 | C22 | semidirect |
| 28. #3746⋊C3 | C22 | semidirect |
| 29. #88433 | C22 | semidirect |
| 30. #88431 | C22 | semidirect |
| 35. C2×#3746 | D3 | semidirect |
| 36. C2×#3744 | D3 | semidirect |
| 104. #3746 | C2×D3 | semidirect |
| 105. #3744 | C2×D3 | semidirect |
| 208. C2×H(3,𝔽3) | #137 | semidirect |
| 312. H(3,𝔽3) | C2×#137 | semidirect |
| 391. C2×C32 | #915 | semidirect |
| 392. C2×C32 | #918 | semidirect |
| 460. C32 | C2×#915 | semidirect |
| 461. C32 | C2×#918 | semidirect |
| 517. C2 | #11720845 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88651 | 2 |
| C2×#88649 | 2 |
| C2×#88527 | 2 |
| C2×#3744⋊C3 | 2 |
| C2×#3746⋊C3 | 2 |
| C2×#88433 | 2 |
| C2×#88431 | 2 |
| #11720845 | 2 |
| C2×#63801 | 3 |
| C2×#63800 | 3 |