Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
504 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 182 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 |
|---|---|---|
| 67. Q8×C9 | Q16 | semidirect |
| 177. C9 | #3363 | semidirect |
| 183. Q8 | Dic36 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589672 | 2 |
| Q8×Dic18 | 2 |
| C8×Q8×C9 | 2 |
| #10588514 | 2 |
| #10588513 | 2 |
| C4×Dic36 | 2 |
| #10588361 | 2 |
| #79933 | 3 |