Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
606 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 233 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. #10589413 | C2 | semidirect |
| 114. C32 | #1544 | semidirect |
| 136. C3 | #71829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#533 | 2 |
| #10592624 | 2 |
| #10589413 | 2 |
| #71829 | 3 |