Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1419 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1419 conjugacy classes of subgroups — too many to draw. Only its 349 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×C4×#1084 | C2 | semidirect |
| 4. #11720574 | C2 | semidirect |
| 8. C22×C4×H(3,𝔽3) | C4 | semidirect |
| 12. #88552 | C4 | direct (N × H) |
| 30. C2×#1084 | C2×C4 | semidirect |
| 35. C22×C32×C4 | Dic3 | semidirect |
| 44. C22×H(3,𝔽3) | C42 | semidirect |
| 50. C4×H(3,𝔽3) | C22⋊C4 | semidirect |
| 98. C22×C32 | C4×Dic3 | semidirect |
| 104. C32×C4 | #217 | semidirect |
| 110. H(3,𝔽3) | C4×C22⋊C4 | semidirect |
| 145. C22×C4 | #1084 | semidirect |
| 172. C32 | C4×#217 | semidirect |
| 199. C22 | C4×#1084 | semidirect |
| 206. C4 | #88552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×H(3,𝔽3) | 2 |
| C2×#88552 | 2 |
| C2×C4×#1084 | 2 |
| #11720574 | 2 |
| C3×C4×#217 | 3 |