Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
252 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. C9×#475 | C2 | semidirect |
| 4. #10588701 | C2 | semidirect |
| 5. #10588224 | C2 | semidirect |
| 7. #10588156 | C2 | semidirect |
| 86. C9⋊C8 | SD16 | semidirect |
| 88. #475 | D9 | semidirect |
| 196. C9 | #1686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#475 | 2 |
| #10588770 | 2 |
| #10588710 | 2 |
| #10588701 | 2 |
| #10588224 | 2 |
| #10588163 | 2 |
| #10588156 | 2 |
| #71120 | 3 |