Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
486 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 12. C32×#97 | C4 | semidirect |
| 13. C32×C4×C8 | C4 | semidirect |
| 40. C3×#97 | Dic3 | semidirect |
| 41. C3×C4×C8 | Dic3 | semidirect |
| 88. #97 | C3⋊Dic3 | semidirect |
| 89. C4×C8 | C3⋊Dic3 | semidirect |
| 129. C32 | #1841 | semidirect |
| 154. C3 | #69871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×M16 | 2 |
| #10589426 | 2 |
| #10589423 | 2 |
| #10589422 | 2 |
| #10589389 | 2 |
| #69871 | 3 |