Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
764 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 286 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. #10592381 | C3 | direct (N × H) |
| 23. C33×C8 | Q8 | semidirect |
| 64. C32×C8 | Dic6 | semidirect |
| 65. C32×C8 | C3×Q8 | semidirect |
| 99. C33 | #500 | semidirect |
| 114. C3×C8 | C3×Dic6 | semidirect |
| 115. C3×C8 | #634 | semidirect |
| 145. C32 | #4682 | semidirect |
| 146. C32 | C3×#500 | semidirect |
| 152. C8 | C3×#634 | semidirect |
| 168. C3 | C3×#4682 | semidirect |
| 169. C3 | #10592381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64078 | 2 |
| C33×C4×C8 | 2 |
| C3×#63645 | 2 |
| #10592381 | 3 |
| C3×#4682 | 3 |