Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
698 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 5. #10590387 | C3 | direct (N × H) |
| 46. C33×C4 | Q16 | semidirect |
| 112. C32×C4 | #216 | semidirect |
| 113. C32×C4 | C3×Q16 | semidirect |
| 122. C33 | #494 | semidirect |
| 173. C3×C4 | #3718 | semidirect |
| 174. C3×C4 | C3×#216 | semidirect |
| 181. C32 | #5092 | semidirect |
| 182. C32 | C3×#494 | semidirect |
| 200. C4 | C3×#3718 | semidirect |
| 205. C3 | #10590387 | direct (N × H) |
| 206. C3 | C3×#5092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#869 | 2 |
| C2×C3×#3718 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C3×#5092 | 3 |
| #10590387 | 3 |