Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
504 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 139 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. #10592793 | C2 | semidirect |
| 4. #10592378 | C2 | semidirect |
| 5. #10589413 | C2 | semidirect |
| 7. #10589324 | C2 | semidirect |
| 83. C32×C8 | SD16 | semidirect |
| 157. C3×C8 | #214 | semidirect |
| 196. C32 | #1686 | semidirect |
| 217. C8 | #3754 | semidirect |
| 234. C3 | #71273 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#492 | 2 |
| #10592793 | 2 |
| #10592774 | 2 |
| #10592378 | 2 |
| #10589413 | 2 |
| #10589410 | 2 |
| #10589324 | 2 |
| #71273 | 3 |