Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
6044 conjugacy classes of subgroups; only the 2030 normal subgroups are shown.
This group has 6044 conjugacy classes of subgroups — too many to draw. Only its 2030 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. C22×C3×#634 | C2 | direct (N × H) |
| 4. C23×#634 | C3 | direct (N × H) |
| 9. C2×C3×#634 | C22 | direct (N × H) |
| 14. C22×#634 | C2×C3 | direct (N × H) |
| 17. C23×C33 | Q8 | semidirect |
| 21. C3×#634 | C23 | direct (N × H) |
| 31. C2×#634 | C22×C3 | direct (N × H) |
| 34. C22×C33 | C2×Q8 | semidirect |
| 47. C23×C32 | Dic6 | semidirect |
| 48. C23×C32 | C3×Q8 | semidirect |
| 55. #634 | C23×C3 | direct (N × H) |
| 59. C2×C33 | C22×Q8 | semidirect |
| 73. C22×C32 | C2×Dic6 | semidirect |
| 74. C22×C32 | C2×C3×Q8 | semidirect |
| 85. C33 | C23×Q8 | semidirect |
| 88. C23×C3 | C3×Dic6 | semidirect |
| 89. C23×C3 | #634 | direct (N × H) |
| 101. C2×C32 | C22×Dic6 | semidirect |
| 102. C2×C32 | C22×C3×Q8 | semidirect |
| 111. C22×C3 | C2×C3×Dic6 | semidirect |
| 112. C22×C3 | C2×#634 | direct (N × H) |
| 121. C32 | C23×Dic6 | semidirect |
| 122. C32 | C23×C3×Q8 | semidirect |
| 123. C23 | C3×#634 | direct (N × H) |
| 130. C2×C3 | C22×C3×Dic6 | semidirect |
| 131. C2×C3 | C22×#634 | direct (N × H) |
| 134. C22 | C2×C3×#634 | direct (N × H) |
| 139. C3 | C23×C3×Dic6 | semidirect |
| 140. C3 | C23×#634 | direct (N × H) |
| 141. C2 | C22×C3×#634 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C33×C4 | 2 |
| C23×C3×C3⋊Dic3 | 2 |
| C22×C3×#634 | 2 |
| C23×#634 | 3 |
| C23×C3×Dic6 | 3 |