Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #10592805 | C2 | semidirect |
| 3. C32×C22⋊C16 | C2 | semidirect |
| 4. #10589375 | C2 | semidirect |
| 5. #10589375 | C2 | semidirect |
| 6. #10589371 | C2 | semidirect |
| 7. #10589370 | C2 | semidirect |
| 22. C3×C22⋊C16 | D3 | semidirect |
| 77. C22⋊C16 | C3⋊D3 | semidirect |
| 169. C32 | #2234 | semidirect |
| 203. C3 | #69097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592814 | 2 |
| #10592805 | 2 |
| C32×C22⋊C16 | 2 |
| #10589375 | 2 |
| #10589371 | 2 |
| #10589370 | 2 |
| #69097 | 3 |