Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
529 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 529 conjugacy classes of subgroups — too many to draw. Only its 115 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. Q8×Q8⋊C9 | C2 | semidirect |
| 2. C4⋊(#41⋊C9) | C2 | semidirect |
| 3. C4×#41⋊C9 | C2 | semidirect |
| 21. #3483 | C9 | semidirect |
| 45. Q8⋊C9 | #41 | semidirect |
| 159. Q8 | #41⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Q8⋊C9 | 2 |
| C4⋊(#41⋊C9) | 2 |
| C4×#41⋊C9 | 2 |
| C3×#3483 | 3 |
| C4×Q8×C9 | 4 |