Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #10592381 | C2 | semidirect |
| 4. #10589352 | C2 | semidirect |
| 5. #10589323 | C2 | semidirect |
| 62. C32×C8 | SD16 | semidirect |
| 117. C3×C8 | #214 | semidirect |
| 147. C32 | #1693 | semidirect |
| 162. C8 | #3754 | semidirect |
| 177. C3 | #70873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#436 | 2 |
| #10592718 | 2 |
| #10592381 | 2 |
| #10589352 | 2 |
| #10589323 | 2 |
| #70873 | 3 |