Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
266 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10592603 | C2 | semidirect |
| 2. C2×C3×D48 | C2 | semidirect |
| 3. C3×#4499 | C2 | semidirect |
| 4. #10589073 | C2 | semidirect |
| 5. #10589071 | C2 | semidirect |
| 11. #63628 | C22 | semidirect |
| 13. #63626 | C22 | semidirect |
| 16. C3×C3⋊C32 | C22 | semidirect |
| 21. C2×D48 | D3 | semidirect |
| 25. #4499 | D3 | semidirect |
| 61. C3⋊C32 | C2×D3 | semidirect |
| 180. C32 | #2263 | semidirect |
| 210. C3 | #69373 | semidirect |
| 211. C3 | #71458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592603 | 2 |
| C2×C3×D48 | 2 |
| C3×#4499 | 2 |
| #10589073 | 2 |
| #10589071 | 2 |
| #71458 | 3 |
| #69373 | 3 |