Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1152 conjugacy classes of subgroups; only the 345 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 345 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. #10592768 | C2 | direct (N × H) |
| 118. C2×C32 | #491 | semidirect |
| 144. C32 | C2×#491 | semidirect |
| 158. C2×C3 | #5069 | semidirect |
| 169. C3 | C2×#5069 | semidirect |
| 170. C2 | #10592768 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#125 | 2 |
| C2×#64078 | 2 |
| #10592768 | 2 |
| C2×#63637 | 2 |
| C2×#63630 | 2 |
| C2×#5069 | 3 |