Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
300 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 79. Q8×C9 | Q16 | semidirect |
| 211. C9 | #1645 | semidirect |
| 218. Q8 | #3674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q82×C9 | 2 |
| #10588759 | 2 |
| #10588707 | 2 |
| #10588702 | 2 |
| #10588223 | 2 |
| #10588212 | 2 |
| #71941 | 3 |