Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
339 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 180. C32 | #1676 | semidirect |
| 210. C3 | #71149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊(C3⋊C8) | 2 |
| C3×#5021 | 2 |
| #10590312 | 2 |
| #10589100 | 2 |
| #10589095 | 2 |
| #71149 | 3 |