Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
594 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 191 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. D4×Q8⋊C9 | C2 | semidirect |
| 3. C2×C4×Q8⋊C9 | C2 | semidirect |
| 22. Q8×#41 | C9 | semidirect |
| 48. Q8⋊C9 | #41 | direct (N × H) |
| 49. Q82 | C2×C9 | semidirect |
| 52. D4×Q8 | C2×C9 | semidirect |
| 55. C2×C4×Q8 | C2×C9 | semidirect |
| 125. #41 | Q8⋊C9 | direct (N × H) |
| 164. Q8 | C2×Q8⋊C9 | semidirect |
| 165. Q8 | C9×#41 | semidirect |
| 166. D4 | C2×Q8⋊C9 | semidirect |
| 174. C2×C4 | C2×Q8⋊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 |
| D4×Q8⋊C9 | 2 |
| C2×C4×Q8⋊C9 | 2 |
| C3×Q8×#41 | 3 |
| C2×C9×#41 | 4 |