Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1176 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 311 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. Q8×#634 | C2 | semidirect |
| 3. #10592774 | C2 | semidirect |
| 4. #10592769 | C2 | semidirect |
| 5. Q8×C3⋊(C3⋊C8) | C2 | semidirect |
| 6. C4×#3754 | C2 | semidirect |
| 7. #10592707 | C2 | semidirect |
| 69. C32×Q8 | SD16 | semidirect |
| 83. #634 | #41 | semidirect |
| 140. C3×Q8 | #214 | semidirect |
| 191. C32 | #3362 | semidirect |
| 196. Q8 | #3754 | semidirect |
| 225. C3 | #83586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#550 | 2 |
| Q8×#634 | 2 |
| #10592774 | 2 |
| #10592769 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| C4×#3754 | 2 |
| #10592707 | 2 |
| #83586 | 3 |