Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 385 conjugacy classes of subgroups — too many to draw. Only its 180 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. #10589142 | C2 | direct (N × H) |
| 7. C2×C3⋊(C3⋊C16) | C4 | semidirect |
| 24. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 102. C2×C32 | #367 | semidirect |
| 129. C32 | C2×#367 | semidirect |
| 143. C2×C3 | #4490 | semidirect |
| 155. C3 | C2×#4490 | semidirect |
| 156. C2 | #10589142 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊C16) | 2 |
| C2×C3×#818 | 2 |
| #10589142 | 2 |
| C2×#4490 | 3 |