Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
720 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 321 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 |
|---|---|---|
| 10. C32×#97 | C4 | semidirect |
| 12. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 32. C3×#97 | Dic3 | semidirect |
| 70. #97 | C3⋊Dic3 | semidirect |
| 103. C32 | #1746 | semidirect |
| 124. C3 | #69806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#97 | 2 |
| #10592631 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #10589416 | 2 |
| #69806 | 3 |