Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
358 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. #10590174 | C2 | semidirect |
| 4. #10590148 | C2 | semidirect |
| 9. #63765 | C4 | semidirect |
| 26. #3708 | C2×C4 | semidirect |
| 69. C3⋊Dic3 | M32 | semidirect |
| 114. C32 | C4×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63765 | 2 |
| C4×C8×C3⋊D3 | 2 |
| #10590174 | 2 |
| #10590148 | 2 |
| C4×M32 | 9 |