Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
338 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10592600 | C2 | semidirect |
| 2. C2×C3×D48 | C2 | semidirect |
| 3. #10590929 | C2 | semidirect |
| 4. C3×#4506 | C2 | semidirect |
| 5. #10589126 | C2 | semidirect |
| 21. C2×D48 | D3 | semidirect |
| 28. #4506 | D3 | semidirect |
| 212. C32 | #2221 | semidirect |
| 244. C3 | #69361 | semidirect |
| 245. C3 | #71472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592600 | 2 |
| C2×C3×D48 | 2 |
| #10590929 | 2 |
| C3×#4506 | 2 |
| #10589126 | 2 |
| #71472 | 3 |
| #69361 | 3 |