Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2350 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 2350 conjugacy classes of subgroups — too many to draw. Only its 754 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. #10596644 | C2 | direct (N × H) |
| 3. C2×#64289 | C2 | semidirect |
| 4. C2×#64283 | C2 | semidirect |
| 13. #64289 | C22 | semidirect |
| 14. #64283 | C22 | semidirect |
| 15. C2×#3788 | C22 | semidirect |
| 16. C2×#3787 | C22 | semidirect |
| 34. #3788 | C23 | semidirect |
| 35. #3787 | C23 | semidirect |
| 116. C2×C32 | #568 | semidirect |
| 147. C32 | C2×#568 | semidirect |
| 181. C2 | #10596644 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3832 | 2 |
| #10596644 | 2 |
| C2×#64289 | 2 |
| C2×#64283 | 2 |
| C2×#568 | 9 |