Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
282 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 78 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×#474 | C2 | semidirect |
| 2. #10588770 | C2 | semidirect |
| 4. D4×C9⋊C8 | C2 | semidirect |
| 5. #10588224 | C2 | semidirect |
| 6. #10588163 | C2 | semidirect |
| 7. #10588157 | C2 | semidirect |
| 72. D4×C9 | SD16 | semidirect |
| 89. C9⋊C8 | D8 | semidirect |
| 91. #474 | D9 | semidirect |
| 208. C9 | #1665 | semidirect |
| 219. D4 | #3675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#474 | 2 |
| #10588770 | 2 |
| #10588698 | 2 |
| D4×C9⋊C8 | 2 |
| #10588224 | 2 |
| #10588163 | 2 |
| #10588157 | 2 |
| #71100 | 3 |