Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
322 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 322 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 |
|---|---|---|
| 4. #10590171 | C2 | semidirect |
| 5. #10590170 | C2 | semidirect |
| 26. C32×M16 | C8 | semidirect |
| 55. C32×C8 | C2×C8 | semidirect |
| 119. M16 | #622 | semidirect |
| 142. C32 | #1565 | semidirect |
| 159. C8 | C2×#622 | 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 |
| #10590171 | 2 |
| #10590170 | 2 |
| #1565 | 9 |