Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
213 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10588362 | C2 | semidirect |
| 4. #10588166 | C2 | semidirect |
| 5. C4⋊(C9⋊C16) | C2 | semidirect |
| 25. C9×D8 | Q8 | semidirect |
| 115. D8 | Dic18 | semidirect |
| 134. C9 | #2224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×D8 | 2 |
| #10588362 | 2 |
| #10588239 | 2 |
| #10588166 | 2 |
| C4⋊(C9⋊C16) | 2 |
| #70886 | 3 |