Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
168 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 2. C2×Dic72 | C2 | semidirect |
| 3. #10588197 | C2 | direct (N × H) |
| 4. C2×C9⋊C32 | C2 | semidirect |
| 12. Dic72 | C22 | semidirect |
| 13. C9⋊C32 | C22 | semidirect |
| 82. C2×C9 | SD64 | semidirect |
| 99. C9 | C2×SD64 | semidirect |
| 120. C2 | #10588197 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D16 | 2 |
| C2×Dic72 | 2 |
| #10588197 | 2 |
| C2×C9⋊C32 | 2 |
| C2×#4520 | 3 |