Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
456 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 179. C32 | #1587 | semidirect |
| 211. C3 | #68222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3756 | 2 |
| #10592723 | 2 |
| #10592529 | 2 |
| C32×Q8⋊C8 | 2 |
| #10589346 | 2 |
| #10589322 | 2 |
| #10589321 | 2 |
| #68222 | 3 |