Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1050 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 285 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. #10596224 | C2 | semidirect |
| 2. C32×#504 | C2 | semidirect |
| 3. #10592608 | C2 | semidirect |
| 4. C2×#63628 | C2 | semidirect |
| 5. #10592603 | C2 | semidirect |
| 19. C3×#504 | D3 | semidirect |
| 63. #504 | C3⋊D3 | semidirect |
| 125. C32 | #3417 | semidirect |
| 145. C3 | #82015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596224 | 2 |
| C32×#504 | 2 |
| #10592608 | 2 |
| C2×#63628 | 2 |
| #10592603 | 2 |
| #82015 | 3 |