Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1044 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1044 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. C2×C32×#137 | C2 | semidirect |
| 3. #10596287 | C2 | semidirect |
| 4. #10592939 | C2 | semidirect |
| 5. #10592924 | C2 | semidirect |
| 6. #10592838 | C2 | semidirect |
| 7. #10589425 | C2 | semidirect |
| 32. C2×C3×#137 | D3 | semidirect |
| 146. C2×#137 | C3⋊D3 | semidirect |
| 341. C32 | #2009 | semidirect |
| 403. C3 | #72111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#137 | 2 |
| #10596293 | 2 |
| #10596287 | 2 |
| #10592939 | 2 |
| #10592924 | 2 |
| #10592838 | 2 |
| #10589425 | 2 |
| #72111 | 3 |