Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
979 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 979 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 3. C2×#3746⋊C3 | C2 | semidirect |
| 4. C2×#88433 | C2 | semidirect |
| 5. #11720833 | C2 | direct (N × H) |
| 16. #3746⋊C3 | C22 | semidirect |
| 17. #88433 | C22 | semidirect |
| 19. C2×#3746 | D3 | semidirect |
| 49. #3746 | C2×D3 | semidirect |
| 57. C2×#272 | Q16 | semidirect |
| 98. C2×H(3,𝔽3) | C2×Q16 | semidirect |
| 100. #272 | C2×Q16 | semidirect |
| 148. H(3,𝔽3) | C22×Q16 | semidirect |
| 185. C2×C32 | D3×Q16 | semidirect |
| 222. C32 | C2×D3×Q16 | semidirect |
| 255. C2 | #11720833 | 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×C8×#272 | 2 |
| C2×#3746⋊C3 | 2 |
| C2×#88433 | 2 |
| #11720833 | 2 |
| C2×D3×Dic12 | 3 |