Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
360 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 66 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×#63736 | C2 | direct (N × H) |
| 4. C2×#63736 | C3 | direct (N × H) |
| 13. #63736 | C2×C3 | direct (N × H) |
| 60. C2×C33 | Q32 | semidirect |
| 89. C33 | C2×Q32 | semidirect |
| 113. C2×C32 | C3×Q32 | semidirect |
| 135. C32 | C2×C3×Q32 | semidirect |
| 146. C2×C3 | #63736 | direct (N × H) |
| 154. C3 | C2×#63736 | direct (N × H) |
| 155. C2 | C3×#63736 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3718 | 2 |
| C2×C3×#3708 | 2 |
| C3×#63736 | 2 |
| C2×#63736 | 3 |
| C2×C3×Q32 | 9 |