Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 59. C32×C8 | Q16 | semidirect |
| 109. C3×C8 | #216 | semidirect |
| 135. C32 | #1694 | semidirect |
| 148. C8 | #3756 | semidirect |
| 160. C3 | #70964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#446 | 2 |
| #10592730 | 2 |
| #10592381 | 2 |
| #10589352 | 2 |
| #10589323 | 2 |
| #70964 | 3 |