Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2724 conjugacy classes of subgroups; only the 705 normal subgroups are shown.
This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 705 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. #10592929 | C2 | direct (N × H) |
| 27. C22×C3⋊Dic3 | Q8 | semidirect |
| 53. C2×C3⋊Dic3 | C2×Q8 | semidirect |
| 102. C2×C32 | #395 | semidirect |
| 128. C32 | C2×#395 | semidirect |
| 143. C2×C3 | #5230 | semidirect |
| 156. C3 | C2×#5230 | semidirect |
| 157. C2 | #10592929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×Q8 | 2 |
| C22×#3750 | 2 |
| #10592929 | 2 |
| C2×#63658 | 2 |
| C2×#5230 | 3 |