Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
798 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 798 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. #10592623 | C2 | semidirect |
| 4. #10589325 | C2 | semidirect |
| 5. #10589322 | C2 | semidirect |
| 25. C3×C4×M16 | D3 | semidirect |
| 94. C4⋊(C3⋊D3) | M16 | semidirect |
| 100. #634 | M16 | semidirect |
| 105. C4×M16 | C3⋊D3 | semidirect |
| 251. C32 | #1489 | semidirect |
| 302. C3 | #69854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3828 | 2 |
| C32×C4×M16 | 2 |
| #10592623 | 2 |
| #10589325 | 2 |
| #10589322 | 2 |
| #69854 | 3 |