Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
349 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 122 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×#4682 | C2 | semidirect |
| 3. C32×C4×C16 | C2 | semidirect |
| 4. C3×#4509 | C2 | semidirect |
| 6. #69058 | C3 | direct (N × H) |
| 18. #4682 | C2×C3 | semidirect |
| 21. C3×C4×C16 | D3 | semidirect |
| 22. C3×C4×C16 | C2×C3 | semidirect |
| 23. #4509 | C2×C3 | semidirect |
| 70. C4×C16 | C3×D3 | semidirect |
| 184. C32 | #2240 | semidirect |
| 218. C3 | #69058 | direct (N × H) |
| 219. C3 | C3×#2240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4695 | 2 |
| C3×#4682 | 2 |
| C32×C4×C16 | 2 |
| C3×#4509 | 2 |
| C3×#2240 | 3 |
| #69058 | 3 |