Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
504 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 69. Q8×C9 | Q16 | semidirect |
| 177. C9 | #3363 | semidirect |
| 182. 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 |
| #10589672 | 2 |
| #10588766 | 2 |
| #10588764 | 2 |
| #10588707 | 2 |
| C4×#3674 | 2 |
| Q8×C9⋊C8 | 2 |
| #83707 | 3 |