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. C32×C8×Q8 | C2 | semidirect |
| 4. #10592547 | C2 | semidirect |
| 5. #10592541 | C2 | semidirect |
| 6. #10592393 | C2 | semidirect |
| 7. C4×#3744 | C2 | semidirect |
| 27. C3×C8×Q8 | D3 | semidirect |
| 69. C32×Q8 | SD16 | semidirect |
| 83. #634 | #41 | semidirect |
| 91. C8×Q8 | C3⋊D3 | semidirect |
| 140. C3×Q8 | #204 | semidirect |
| 191. C32 | #3362 | semidirect |
| 196. Q8 | #3744 | semidirect |
| 225. C3 | #79932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596048 | 2 |
| Q8×#634 | 2 |
| C32×C8×Q8 | 2 |
| #10592547 | 2 |
| #10592541 | 2 |
| #10592393 | 2 |
| C4×#3744 | 2 |
| #79932 | 3 |