Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1200 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 321 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. #10595941 | C2 | semidirect |
| 3. C2×C32×C4×C8 | C2 | semidirect |
| 4. #10592812 | C2 | semidirect |
| 5. #10592396 | C2 | semidirect |
| 6. #10592393 | C2 | semidirect |
| 7. #10592380 | C2 | semidirect |
| 28. C2×C3×C4×C8 | D3 | semidirect |
| 95. C2×C4×C8 | C3⋊D3 | semidirect |
| 198. C32 | #3131 | semidirect |
| 231. C3 | #78463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595948 | 2 |
| #10595941 | 2 |
| C2×C32×C4×C8 | 2 |
| #10592812 | 2 |
| #10592396 | 2 |
| #10592393 | 2 |
| #10592380 | 2 |
| #78463 | 3 |