Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
345 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C2×C32×D16 | C2 | semidirect |
| 2. C3×#5160 | C2 | semidirect |
| 3. C3×#4901 | C2 | semidirect |
| 4. C3×#4563 | C2 | semidirect |
| 5. C3×#4506 | C2 | semidirect |
| 7. #71472 | C3 | direct (N × H) |
| 20. C2×C3×D16 | D3 | semidirect |
| 21. C2×C3×D16 | C2×C3 | semidirect |
| 24. #5160 | C2×C3 | semidirect |
| 25. #4901 | C2×C3 | semidirect |
| 28. #4563 | C2×C3 | semidirect |
| 29. #4506 | C2×C3 | semidirect |
| 83. C2×D16 | C3×D3 | semidirect |
| 207. C32 | #2221 | semidirect |
| 239. C3 | #71472 | direct (N × H) |
| 240. C3 | C3×#2221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| C3×#5160 | 2 |
| C3×#4901 | 2 |
| C3×#4563 | 2 |
| C3×#4506 | 2 |
| C3×#2221 | 3 |
| #71472 | 3 |