Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
468 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 257 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. #10589371 | C2 | semidirect |
| 5. #10589370 | C2 | semidirect |
| 10. C32×M32 | C4 | semidirect |
| 34. C32×C16 | C2×C4 | semidirect |
| 39. C3×M32 | Dic3 | semidirect |
| 75. C3×C16 | C2×Dic3 | semidirect |
| 89. M32 | C3⋊Dic3 | semidirect |
| 124. C16 | C2×C3⋊Dic3 | semidirect |
| 135. C32 | #2159 | semidirect |
| 162. C3 | #71428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M32 | 2 |
| #10592805 | 2 |
| C2×#63645 | 2 |
| #10589371 | 2 |
| #10589370 | 2 |
| #71428 | 3 |