Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
552 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 169 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 |
|---|---|---|
| 112. C32 | #1293 | semidirect |
| 143. C3 | #67679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C22⋊C8 | 2 |
| #10592906 | 2 |
| #67679 | 3 |