Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4250 conjugacy classes of subgroups; only the 1487 normal subgroups are shown.
This group has 4250 conjugacy classes of subgroups — too many to draw. Only its 1487 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×#6226 | C2 | direct (N × H) |
| 9. C2×#6226 | C22 | direct (N × H) |
| 16. C23×C3×C9 | Q8 | semidirect |
| 20. #6226 | C23 | direct (N × H) |
| 31. C22×C3×C9 | C2×Q8 | semidirect |
| 46. C23×C9 | Dic6 | semidirect |
| 52. C2×C3×C9 | C22×Q8 | semidirect |
| 66. C22×C9 | C2×Dic6 | semidirect |
| 73. C3×C9 | C23×Q8 | semidirect |
| 74. C23×C3 | Dic18 | semidirect |
| 86. C2×C9 | C22×Dic6 | semidirect |
| 92. C22×C3 | C2×Dic18 | semidirect |
| 101. C9 | C23×Dic6 | semidirect |
| 102. C23 | #6226 | direct (N × H) |
| 107. C2×C3 | C22×Dic18 | semidirect |
| 111. C22 | C2×#6226 | direct (N × H) |
| 115. C3 | C23×Dic18 | semidirect |
| 117. C2 | C22×#6226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4×C9 | 2 |
| C23×C3⋊Dic9 | 2 |
| C22×#6226 | 2 |
| C23×#634 | 3 |
| C23×Dic18 | 3 |