Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3612 conjugacy classes of subgroups; only the 1079 normal subgroups are shown.
This group has 3612 conjugacy classes of subgroups — too many to draw. Only its 1079 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. C2×#88864 | C2 | semidirect |
| 3. C2×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 4. C2×C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 9. C2×C33×D4 | C4 | semidirect |
| 34. C2×C3⋊(C3⋊Dic3) | D4 | semidirect |
| 39. C2×C32×D4 | Dic3 | semidirect |
| 56. C33×C4 | C22⋊C4 | semidirect |
| 88. C2×C3×D4 | C3⋊Dic3 | semidirect |
| 105. C32×C4 | #217 | semidirect |
| 112. C33 | #390 | semidirect |
| 137. C2×D4 | C3⋊(C3⋊Dic3) | semidirect |
| 154. C3×C4 | #3757 | semidirect |
| 157. C32 | #5221 | semidirect |
| 191. C4 | #88864 | semidirect |
| 192. C3 | #10592920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×D4 | 2 |
| C2×#88864 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #10592920 | 3 |