Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
258 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 4. #10590136 | C2 | semidirect |
| 8. #63773 | C4 | semidirect |
| 12. #63764 | C4 | semidirect |
| 13. C32×M32 | C4 | semidirect |
| 14. #63639 | C4 | semidirect |
| 16. C16×C3⋊D3 | C4 | semidirect |
| 31. #3708 | C2×C4 | semidirect |
| 32. C32×C16 | C2×C4 | semidirect |
| 33. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 83. M32 | #157 | semidirect |
| 102. C3⋊D3 | #347 | semidirect |
| 118. C16 | C2×#157 | semidirect |
| 127. C32 | C2×#347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63767 | 2 |
| #10593762 | 2 |
| C3⋊D3×M32 | 2 |
| #10590136 | 2 |
| C2×#347 | 9 |