Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
234 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 50. Q8×C9 | Q16 | semidirect |
| 142. C9 | #1670 | semidirect |
| 146. Q8 | Dic36 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×C9 | 2 |
| #10588702 | 2 |
| #10588365 | 2 |
| #10588159 | 2 |
| #10588135 | 2 |
| #70942 | 3 |