Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
316 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 76 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×C3×D48 | C2 | semidirect |
| 2. C3×#4901 | C2 | semidirect |
| 3. #10590926 | C2 | semidirect |
| 4. #10589372 | C2 | semidirect |
| 5. #10589127 | C2 | semidirect |
| 23. C2×D48 | D3 | semidirect |
| 24. #4901 | D3 | semidirect |
| 199. C32 | #2221 | semidirect |
| 230. C3 | #71454 | semidirect |
| 231. C3 | #71472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D48 | 2 |
| C3×#4901 | 2 |
| #10590926 | 2 |
| #10589372 | 2 |
| #10589127 | 2 |
| #71472 | 3 |
| #71454 | 3 |