Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
869 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 869 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 2. #11721826 | C2 | semidirect |
| 3. #11720580 | C2 | semidirect |
| 7. C2×Q8×H(3,𝔽3) | C4 | semidirect |
| 8. C2×D4×H(3,𝔽3) | C4 | semidirect |
| 10. C22×C4×H(3,𝔽3) | C4 | semidirect |
| 35. C2×C32×Q8 | Dic3 | semidirect |
| 36. C2×C32×D4 | Dic3 | semidirect |
| 38. C22×C32×C4 | Dic3 | semidirect |
| 110. H(3,𝔽3) | #410 | semidirect |
| 143. C2×Q8 | #1084 | semidirect |
| 144. C2×D4 | #1084 | semidirect |
| 146. C22×C4 | #1084 | semidirect |
| 171. C32 | #5240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×H(3,𝔽3) | 2 |
| #11721826 | 2 |
| #11720580 | 2 |
| C3×#5240 | 3 |