Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
249 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #10588359 | C2 | semidirect |
| 5. #10588160 | C2 | semidirect |
| 6. #10588157 | C2 | semidirect |
| 7. C8×C9⋊C8 | C2 | semidirect |
| 80. C8×C9 | SD16 | semidirect |
| 84. C9⋊C8 | M16 | semidirect |
| 191. C9 | #1590 | semidirect |
| 211. C8 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#436 | 2 |
| C4×#3672 | 2 |
| #10588359 | 2 |
| D4⋊(C9⋊C8) | 2 |
| #10588160 | 2 |
| #10588157 | 2 |
| C8×C9⋊C8 | 2 |
| #70866 | 3 |