Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
330 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 121 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×C16 | C2 | semidirect |
| 3. #10589324 | C2 | semidirect |
| 13. C3×C4×C16 | D3 | semidirect |
| 24. #3745 | C8 | semidirect |
| 48. C4×C16 | C3⋊D3 | semidirect |
| 116. C32 | #1331 | semidirect |
| 144. C3 | #67504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| C32×C4×C16 | 2 |
| #10589324 | 2 |
| #67504 | 3 |