Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
321 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 98 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. #10588760 | C2 | semidirect |
| 4. #10588360 | C2 | semidirect |
| 5. C8×C9⋊C8 | C2 | semidirect |
| 52. C8×C9 | SD16 | semidirect |
| 53. C9⋊C8 | SD16 | semidirect |
| 120. C9 | #1705 | semidirect |
| 131. C8 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#492 | 2 |
| #10588760 | 2 |
| #10588753 | 2 |
| #10588360 | 2 |
| C8×C9⋊C8 | 2 |
| #71254 | 3 |