Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
342 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #10590173 | C2 | semidirect |
| 4. #10590170 | C2 | semidirect |
| 29. C8×C3⋊D3 | C8 | semidirect |
| 136. C32 | #1564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593727 | 2 |
| C4×C8×C3⋊D3 | 2 |
| #10590173 | 2 |
| #10590170 | 2 |
| #1564 | 9 |