Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
234 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 68. Q8×C9 | Q16 | semidirect |
| 182. C9 | #1670 | semidirect |
| 188. Q8 | #3674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#475 | 2 |
| #10588765 | 2 |
| #10588702 | 2 |
| Q8×C9⋊C8 | 2 |
| #10588224 | 2 |
| #10588161 | 2 |
| #10588156 | 2 |
| #71117 | 3 |