Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
575 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 575 conjugacy classes of subgroups — too many to draw. Only its 112 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×#5119 | C2 | semidirect |
| 3. #10591231 | C2 | semidirect |
| 4. #10591084 | C2 | semidirect |
| 5. #10589423 | C2 | semidirect |
| 25. #5119 | D3 | semidirect |
| 277. C32 | #2053 | semidirect |
| 320. C3 | #70547 | semidirect |
| 321. C3 | #72115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| C3×#5119 | 2 |
| #10591231 | 2 |
| #10591084 | 2 |
| #10589423 | 2 |
| #72115 | 3 |
| #70547 | 3 |