Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
876 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 876 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. C2×C32×#108 | C2 | semidirect |
| 3. C2×#63652 | C2 | semidirect |
| 4. #10592828 | C2 | semidirect |
| 5. C2×#63642 | C2 | semidirect |
| 12. C2×#3746 | C4 | semidirect |
| 15. C2×#3745 | C4 | semidirect |
| 16. C2×#3744 | C4 | semidirect |
| 22. C2×C3×#108 | D3 | semidirect |
| 90. C2×#108 | C3⋊D3 | semidirect |
| 210. C32 | #1975 | semidirect |
| 251. C3 | #70697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64113 | 2 |
| C2×C32×#108 | 2 |
| C2×#63652 | 2 |
| #10592828 | 2 |
| C2×#63642 | 2 |
| #70697 | 3 |