Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 341 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 |
|---|---|---|
| 2. C3×#4683 | C2 | semidirect |
| 3. C3×#4564 | C2 | semidirect |
| 5. C3×C4×C3⋊C16 | C2 | semidirect |
| 7. #71318 | C3 | direct (N × H) |
| 21. #4683 | C2×C3 | semidirect |
| 25. #4564 | C2×C3 | semidirect |
| 27. C4×C3⋊C16 | C2×C3 | semidirect |
| 200. C32 | #2242 | semidirect |
| 230. C3 | #71318 | direct (N × H) |
| 231. C3 | C3×#2242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#495 | 2 |
| C3×#4683 | 2 |
| C3×#4564 | 2 |
| C3×#4562 | 2 |
| C3×C4×C3⋊C16 | 2 |
| C3×#2242 | 3 |
| #71318 | 3 |