Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 198 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×Dic72 | C2 | direct (N × H) |
| 10. Dic72 | C22 | direct (N × H) |
| 50. C22×C9 | Q32 | semidirect |
| 69. C2×C9 | C2×Q32 | semidirect |
| 85. C9 | C22×Q32 | semidirect |
| 96. C22 | Dic72 | direct (N × H) |
| 102. C2 | C2×Dic72 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic36 | 2 |
| C22×C9×C16 | 2 |
| C2×Dic72 | 2 |
| C22×Dic24 | 3 |