Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
933 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 933 conjugacy classes of subgroups — too many to draw. Only its 150 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. C22×C32×D8 | C2 | semidirect |
| 2. C2×C3×#932 | C2 | semidirect |
| 3. C2×C3×#833 | C2 | semidirect |
| 4. C3×#5110 | C2 | semidirect |
| 5. C3×#4552 | C2 | semidirect |
| 7. #72046 | C3 | direct (N × H) |
| 23. C22×C3×D8 | D3 | semidirect |
| 24. C22×C3×D8 | C2×C3 | semidirect |
| 25. C2×#932 | C2×C3 | semidirect |
| 28. C2×#833 | C2×C3 | semidirect |
| 29. #5110 | C2×C3 | semidirect |
| 31. #4552 | C2×C3 | semidirect |
| 111. C22×D8 | C3×D3 | semidirect |
| 325. C32 | #2018 | semidirect |
| 377. C3 | #72046 | direct (N × H) |
| 378. C3 | C3×#2018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D8 | 2 |
| C2×C3×#932 | 2 |
| C2×C3×#833 | 2 |
| C3×#5110 | 2 |
| C3×#4552 | 2 |
| C3×#2018 | 3 |
| #72046 | 3 |