Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
156 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 32 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 |
|---|---|---|
| 2. #10590166 | C2 | semidirect |
| 3. C2×#63540 | C2 | semidirect |
| 81. C32 | #1401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592606 | 2 |
| #10590166 | 2 |
| C2×#63540 | 2 |
| #1401 | 9 |