Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
298 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×#63748 | C2 | direct (N × H) |
| 4. C2×#63748 | C3 | direct (N × H) |
| 14. #63748 | C2×C3 | direct (N × H) |
| 64. C2×C33 | #108 | semidirect |
| 97. C33 | C2×#108 | semidirect |
| 125. C2×C32 | C3×#108 | semidirect |
| 156. C32 | C2×C3×#108 | semidirect |
| 176. C2×C3 | #63748 | direct (N × H) |
| 188. C3 | C2×#63748 | direct (N × H) |
| 191. C2 | C3×#63748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3792 | 2 |
| C22×C3×#622 | 2 |
| C3×#63748 | 2 |
| C2×#63748 | 3 |
| C2×C3×#108 | 9 |