Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
936 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 233 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×#431 | C2 | semidirect |
| 3. #10592623 | C2 | semidirect |
| 4. #10589325 | C2 | semidirect |
| 18. C32×C4×C8 | C22 | semidirect |
| 20. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 22. C3×#431 | D3 | semidirect |
| 61. C3×C4×C8 | C2×D3 | semidirect |
| 83. C4⋊(C3⋊D3) | M16 | semidirect |
| 90. #431 | C3⋊D3 | semidirect |
| 146. C4×C8 | C2×C3⋊D3 | semidirect |
| 216. C32 | #1486 | semidirect |
| 263. C3 | #70762 | 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×#431 | 2 |
| #10592623 | 2 |
| #10589325 | 2 |
| #70762 | 3 |