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 |
|---|---|---|
| 2. #10588753 | C2 | semidirect |
| 3. #10588690 | C2 | semidirect |
| 4. D4×C9⋊C8 | C2 | semidirect |
| 5. #10588221 | C2 | semidirect |
| 6. #10588161 | C2 | semidirect |
| 7. #10588157 | C2 | semidirect |
| 75. D4×C9 | SD16 | semidirect |
| 89. C9⋊C8 | D8 | semidirect |
| 208. C9 | #1665 | semidirect |
| 219. D4 | #3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#459 | 2 |
| #10588753 | 2 |
| #10588690 | 2 |
| D4×C9⋊C8 | 2 |
| #10588221 | 2 |
| #10588161 | 2 |
| #10588157 | 2 |
| #71004 | 3 |