Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
306 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #10589329 | C2 | semidirect |
| 84. C32 | #1359 | semidirect |
| 103. C3 | #67787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#492 | 2 |
| #10589329 | 2 |
| #67787 | 3 |