Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
532 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 86 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. C3×#4751 | C2 | semidirect |
| 3. #10591637 | C2 | semidirect |
| 4. #10589343 | C2 | semidirect |
| 5. C3×#4478 | C2 | semidirect |
| 6. #10589184 | C2 | semidirect |
| 7. #10589183 | C2 | semidirect |
| 34. #4751 | D3 | semidirect |
| 38. #4478 | D3 | semidirect |
| 435. C32 | #2132 | semidirect |
| 503. C3 | #69172 | semidirect |
| 504. C3 | #70148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595360 | 2 |
| C3×#4751 | 2 |
| #10591637 | 2 |
| #10589343 | 2 |
| C3×#4478 | 2 |
| #10589184 | 2 |
| #10589183 | 2 |
| #70148 | 3 |
| #69172 | 3 |