Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
780 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 257 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. C2×#63639 | C2 | semidirect |
| 4. #10589428 | C2 | semidirect |
| 9. C2×C32×D8 | C4 | semidirect |
| 13. #63645 | C22 | semidirect |
| 16. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 42. C2×C3×D8 | Dic3 | semidirect |
| 99. C2×D8 | C3⋊Dic3 | semidirect |
| 153. C32 | #2140 | semidirect |
| 183. C3 | #72033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D8 | 2 |
| #10592805 | 2 |
| C2×#63639 | 2 |
| #10589428 | 2 |
| #72033 | 3 |