Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
530 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 6. #10590900 | C3 | direct (N × H) |
| 28. C33×C8 | Q8 | semidirect |
| 29. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 84. C32×C8 | Dic6 | semidirect |
| 85. C32×C8 | C3×Q8 | semidirect |
| 86. C3⋊(C3⋊C8) | C3×Q8 | semidirect |
| 137. C33 | #498 | semidirect |
| 156. C3×C8 | #627 | semidirect |
| 157. C3×C8 | C3×Dic6 | semidirect |
| 201. C32 | #4855 | semidirect |
| 202. C32 | C3×#498 | semidirect |
| 208. C8 | C3×#627 | semidirect |
| 227. C3 | #10590900 | direct (N × H) |
| 228. C3 | C3×#4855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63919 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| C32×#817 | 2 |
| C3×#63574 | 2 |
| C3×#4855 | 3 |
| #10590900 | 3 |