Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
936 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 210 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 |
|---|---|---|
| 3. C2×C3×#3776 | C2 | direct (N × H) |
| 4. C22×#3776 | C3 | direct (N × H) |
| 10. C3×#3776 | C22 | direct (N × H) |
| 14. C2×#3776 | C2×C3 | direct (N × H) |
| 34. #3776 | C22×C3 | direct (N × H) |
| 35. C22×C33 | Q16 | semidirect |
| 61. C2×C33 | C2×Q16 | semidirect |
| 79. C22×C32 | C3×Q16 | semidirect |
| 92. C33 | C22×Q16 | semidirect |
| 113. C2×C32 | C2×C3×Q16 | semidirect |
| 125. C22×C3 | #3776 | direct (N × H) |
| 137. C32 | C22×C3×Q16 | semidirect |
| 149. C2×C3 | C2×#3776 | direct (N × H) |
| 151. C22 | C3×#3776 | direct (N × H) |
| 158. C3 | C22×#3776 | direct (N × H) |
| 159. C2 | C2×C3×#3776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#627 | 2 |
| C22×C3×#622 | 2 |
| C2×C3×#3776 | 2 |
| C22×#3776 | 3 |
| C22×C3×Q16 | 9 |