Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
322 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 4. #10590173 | C2 | semidirect |
| 5. #10590172 | C2 | semidirect |
| 32. #3748 | C8 | semidirect |
| 56. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 142. C32 | #1565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593795 | 2 |
| C2×C4⋊#622 | 2 |
| M16×C3⋊Dic3 | 2 |
| #10590173 | 2 |
| #10590172 | 2 |
| #1565 | 9 |