Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
876 conjugacy classes of subgroups; only the 329 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 329 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. C2×#63646 | C2 | semidirect |
| 4. #10589418 | C2 | semidirect |
| 81. C22×C32 | #108 | semidirect |
| 135. C22×C3 | #819 | semidirect |
| 142. C32 | #1810 | semidirect |
| 167. C22 | #63646 | semidirect |
| 174. C3 | #71977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×C8 | 2 |
| #10592906 | 2 |
| C2×#63646 | 2 |
| #10589418 | 2 |
| #71977 | 3 |