Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 305 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 305 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 |
|---|---|---|
| 8. C32×C4×C8 | C4 | semidirect |
| 25. C3×C4×C8 | Dic3 | semidirect |
| 57. C4×C8 | C3⋊Dic3 | semidirect |
| 86. C32 | #1835 | semidirect |
| 106. C3 | #69763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×C8 | 2 |
| #10592635 | 2 |
| #10589417 | 2 |
| #69763 | 3 |