Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1419 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 301 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 |
|---|---|---|
| 4. C2×C4×#1084 | C2 | semidirect |
| 5. #11720574 | C2 | semidirect |
| 10. C22×#1084 | C4 | semidirect |
| 14. C22⋊C4×H(3,𝔽3) | C4 | semidirect |
| 15. #88552 | C4 | semidirect |
| 30. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 37. C2×#1084 | C2×C4 | semidirect |
| 48. C32×C22⋊C4 | Dic3 | semidirect |
| 55. C22×H(3,𝔽3) | C42 | semidirect |
| 64. #1084 | C22⋊C4 | direct (N × H) |
| 83. C2×C32×C4 | C2×Dic3 | semidirect |
| 123. C22×C32 | C4×Dic3 | semidirect |
| 138. H(3,𝔽3) | C4×C22⋊C4 | semidirect |
| 187. C22⋊C4 | #1084 | direct (N × H) |
| 217. C32 | Dic3×C22⋊C4 | semidirect |
| 234. C2×C4 | C2×#1084 | semidirect |
| 251. C22 | C4×#1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1084 | 2 |
| C2×C22⋊C4×H(3,𝔽3) | 2 |
| C2×#88552 | 2 |
| C2×C4×#1084 | 2 |
| #11720574 | 2 |
| C3×Dic3×C22⋊C4 | 3 |