Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1110 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 1110 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. #10596041 | C2 | semidirect |
| 3. #10592793 | C2 | semidirect |
| 4. #10592792 | C2 | semidirect |
| 5. Q8×C3⋊(C3⋊C8) | C2 | semidirect |
| 70. C32×Q8 | SD16 | semidirect |
| 139. C3×Q8 | #214 | semidirect |
| 187. C32 | #3359 | semidirect |
| 192. Q8 | #3754 | semidirect |
| 219. C3 | #83568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D4×Q8 | 2 |
| #10596041 | 2 |
| #10592793 | 2 |
| #10592792 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10592718 | 2 |
| C4×#3754 | 2 |
| #83568 | 3 |