Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
766 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 212 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×#622 | C2 | semidirect |
| 3. #10593749 | C2 | semidirect |
| 4. #10593727 | C2 | semidirect |
| 5. C4×#3787 | C2 | semidirect |
| 21. #3832 | C8 | semidirect |
| 45. C32×Q8 | C2×C8 | semidirect |
| 52. C4⋊(C3⋊D3) | C2×C8 | semidirect |
| 55. C4×C3⋊D3 | C2×C8 | semidirect |
| 57. #622 | #41 | semidirect |
| 141. C32 | C8×#41 | semidirect |
| 143. Q8 | #3787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3832 | 2 |
| Q8×#622 | 2 |
| #10593749 | 2 |
| #10593727 | 2 |
| C4×#3787 | 2 |
| C8×#41 | 9 |