Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
948 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C32×C4×M16 | C2 | semidirect |
| 3. #10592625 | C2 | semidirect |
| 4. #10589325 | C2 | semidirect |
| 17. C32×C4×C8 | C22 | semidirect |
| 19. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 22. C3×C4×M16 | D3 | semidirect |
| 59. C3×C4×C8 | C2×D3 | semidirect |
| 81. C4⋊(C3⋊D3) | M16 | semidirect |
| 88. C4×M16 | C3⋊D3 | semidirect |
| 141. C4×C8 | C2×C3⋊D3 | semidirect |
| 207. C32 | #1490 | semidirect |
| 251. C3 | #69855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊(C3⋊D3) | 2 |
| C32×C4×M16 | 2 |
| #10592625 | 2 |
| #10589325 | 2 |
| #69855 | 3 |