Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
583 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 583 conjugacy classes of subgroups — too many to draw. Only its 153 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. #11721869 | C2 | semidirect |
| 3. #11720586 | C2 | semidirect |
| 4. #11720552 | C2 | semidirect |
| 5. C8×#1084 | C2 | semidirect |
| 8. Q16×H(3,𝔽3) | C4 | semidirect |
| 9. SD16×H(3,𝔽3) | C4 | semidirect |
| 10. D8×H(3,𝔽3) | C4 | semidirect |
| 36. C32×Q16 | Dic3 | semidirect |
| 37. C32×SD16 | Dic3 | semidirect |
| 38. C32×D8 | Dic3 | semidirect |
| 107. H(3,𝔽3) | #443 | semidirect |
| 134. Q16 | #1084 | semidirect |
| 135. SD16 | #1084 | semidirect |
| 136. D8 | #1084 | semidirect |
| 155. C32 | #5196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#135 | 2 |
| #11721869 | 2 |
| #11720586 | 2 |
| #11720552 | 2 |
| C8×#1084 | 2 |
| C3×#5196 | 3 |