Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1026 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 191 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. C22×#3756 | C2 | semidirect |
| 5. C2×#63663 | C2 | semidirect |
| 6. C2×#63651 | C2 | semidirect |
| 7. #10589424 | C2 | semidirect |
| 308. C32 | #2020 | semidirect |
| 362. C3 | #72109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#137 | 2 |
| C2×#64160 | 2 |
| C22×#3756 | 2 |
| #10592933 | 2 |
| C2×#63663 | 2 |
| C2×#63651 | 2 |
| #10589424 | 2 |
| #72109 | 3 |