Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
660 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 660 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 |
|---|---|---|
| 4. #10589430 | C2 | semidirect |
| 9. C2×C32×Q16 | C4 | semidirect |
| 42. C2×C3×Q16 | Dic3 | semidirect |
| 96. C2×Q16 | C3⋊Dic3 | semidirect |
| 146. C32 | #2141 | semidirect |
| 172. C3 | #72061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q16 | 2 |
| #10592805 | 2 |
| C2×#63639 | 2 |
| #10589430 | 2 |
| #72061 | 3 |