Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
850 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 186 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. #10590182 | C2 | direct (N × H) |
| 8. C2×C4⋊#157 | C4 | semidirect |
| 10. C22×C32×C8 | C4 | semidirect |
| 11. C22×C3⋊(C3⋊C8) | C4 | semidirect |
| 13. C2×C8×C3⋊D3 | C4 | semidirect |
| 31. C4⋊#157 | C2×C4 | semidirect |
| 33. C2×C32×C8 | C2×C4 | semidirect |
| 35. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 114. C22×C8 | #157 | semidirect |
| 141. C2×C32 | #340 | semidirect |
| 145. C3⋊D3 | #340 | semidirect |
| 166. C2×C8 | C2×#157 | semidirect |
| 188. C32 | C2×#340 | semidirect |
| 245. C2 | #10590182 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#157 | 2 |
| C22×C8×C3⋊D3 | 2 |
| #10590182 | 2 |
| C2×#340 | 9 |