Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1110 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1110 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. #10596041 | C2 | semidirect |
| 3. C32×C8×Q8 | C2 | semidirect |
| 4. #10592550 | C2 | semidirect |
| 7. #10592380 | C2 | semidirect |
| 27. C3×C8×Q8 | D3 | semidirect |
| 69. C32×Q8 | SD16 | semidirect |
| 89. C8×Q8 | C3⋊D3 | semidirect |
| 138. C3×Q8 | #204 | semidirect |
| 187. C32 | #3359 | semidirect |
| 192. Q8 | #3744 | semidirect |
| 219. C3 | #79925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C4⋊(C3⋊D3) | 2 |
| #10596041 | 2 |
| C32×C8×Q8 | 2 |
| #10592550 | 2 |
| #10592540 | 2 |
| C4×#3744 | 2 |
| #10592380 | 2 |
| #79925 | 3 |