Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1265 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 1265 conjugacy classes of subgroups — too many to draw. Only its 192 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×#63802 | C2 | semidirect |
| 3. C2×#63796 | C2 | semidirect |
| 4. #10594009 | C2 | semidirect |
| 5. C4×C8×C3⋊D3 | C2 | semidirect |
| 6. C3×#4696 | C2 | semidirect |
| 7. #10590869 | C2 | semidirect |
| 8. #10590867 | C2 | semidirect |
| 9. #10590353 | C2 | semidirect |
| 16. C2×C3×Dic12 | C22 | semidirect |
| 18. C2×C3×#204 | C22 | semidirect |
| 19. C3×#875 | C22 | semidirect |
| 22. #63863 | C22 | semidirect |
| 23. C2×#3718 | C22 | semidirect |
| 24. C2×#3715 | C22 | semidirect |
| 29. C32×C4×C8 | C22 | semidirect |
| 30. C8×C3⋊Dic3 | C22 | semidirect |
| 31. C8×C3⋊Dic3 | C22 | semidirect |
| 32. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 42. #4696 | D3 | semidirect |
| 90. C2×Dic12 | C2×D3 | semidirect |
| 92. C2×#204 | C2×D3 | semidirect |
| 99. #875 | C2×D3 | semidirect |
| 103. C3×C4×C8 | C2×D3 | semidirect |
| 223. C4×C8 | D32 | semidirect |
| 267. C3⋊D3 | #495 | semidirect |
| 321. C32 | C2×#495 | semidirect |
| 366. C3 | D3×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63802 | 2 |
| C2×#63797 | 2 |
| C2×#63796 | 2 |
| #10594009 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C3×#4696 | 2 |
| #10590869 | 2 |
| #10590867 | 2 |
| #10590353 | 2 |
| D3×#495 | 3 |