Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
396 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 193 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 |
|---|---|---|
| 7. C2×C32×C16 | C4 | semidirect |
| 9. #63644 | C4 | semidirect |
| 25. C2×C3×C16 | Dic3 | semidirect |
| 58. C2×C16 | C3⋊Dic3 | semidirect |
| 89. C32 | #1384 | semidirect |
| 109. C3 | #67818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M32 | 2 |
| #10592805 | 2 |
| #67818 | 3 |