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. #10592932 | C2 | semidirect |
| 4. #10592778 | C2 | semidirect |
| 5. #10592769 | C2 | semidirect |
| 6. #10592755 | C2 | semidirect |
| 7. C2×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 198. C32 | #3131 | semidirect |
| 231. C3 | #83281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#532 | 2 |
| #10595941 | 2 |
| #10592932 | 2 |
| #10592778 | 2 |
| #10592769 | 2 |
| #10592755 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #83281 | 3 |