Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
768 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 221 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. #10592625 | C2 | semidirect |
| 3. C2×#63630 | C2 | semidirect |
| 4. #10589406 | C2 | semidirect |
| 196. C32 | #1530 | semidirect |
| 236. C3 | #71798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#532 | 2 |
| #10592625 | 2 |
| C2×#63630 | 2 |
| #10589406 | 2 |
| #71798 | 3 |