Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1456 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1456 conjugacy classes of subgroups — too many to draw. Only its 573 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. #11723989 | C2 | semidirect |
| 3. #11722207 | C2 | semidirect |
| 4. #11722189 | C2 | semidirect |
| 5. #11722185 | C2 | semidirect |
| 8. C33×Q16 | C4 | semidirect |
| 9. C33×SD16 | C4 | semidirect |
| 10. C33×D8 | C4 | semidirect |
| 34. C32×Q16 | Dic3 | semidirect |
| 35. C32×SD16 | Dic3 | semidirect |
| 36. C32×D8 | Dic3 | semidirect |
| 69. C3×Q16 | C3⋊Dic3 | semidirect |
| 70. C3×SD16 | C3⋊Dic3 | semidirect |
| 71. C3×D8 | C3⋊Dic3 | semidirect |
| 89. C33 | #444 | semidirect |
| 104. Q16 | C3⋊(C3⋊Dic3) | semidirect |
| 105. SD16 | C3⋊(C3⋊Dic3) | semidirect |
| 106. D8 | C3⋊(C3⋊Dic3) | semidirect |
| 119. C32 | #5197 | semidirect |
| 139. C3 | #10592896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#135 | 2 |
| #11723989 | 2 |
| #11722207 | 2 |
| #11722189 | 2 |
| #11722185 | 2 |
| #10592896 | 3 |