Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3242 conjugacy classes of subgroups; only the 634 normal subgroups are shown.
This group has 3242 conjugacy classes of subgroups — too many to draw. Only its 634 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. C2×#63781 | C2 | direct (N × H) |
| 7. C23×#157 | C4 | semidirect |
| 9. C23×C32×C4 | C4 | semidirect |
| 10. C23×C3⋊Dic3 | C4 | semidirect |
| 12. C22×C4×C3⋊D3 | C4 | semidirect |
| 14. #63781 | C22 | direct (N × H) |
| 26. C22×#157 | C2×C4 | semidirect |
| 29. C22×C32×C4 | C2×C4 | semidirect |
| 31. C22×C3⋊Dic3 | C2×C4 | semidirect |
| 34. C2×C4×C3⋊D3 | C2×C4 | semidirect |
| 61. C2×#157 | C22×C4 | semidirect |
| 63. C2×C32×C4 | C22×C4 | semidirect |
| 65. C2×C3⋊Dic3 | C22×C4 | semidirect |
| 86. C22×C32 | #95 | semidirect |
| 91. C2×C3⋊D3 | #95 | semidirect |
| 113. C23×C4 | #157 | semidirect |
| 136. C2×C32 | C2×#95 | semidirect |
| 140. C3⋊D3 | C2×#95 | semidirect |
| 162. C22×C4 | C2×#157 | semidirect |
| 180. C32 | C22×#95 | semidirect |
| 205. C2×C4 | C22×#157 | semidirect |
| 223. C22 | #63781 | direct (N × H) |
| 235. C2 | C2×#63781 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#157 | 2 |
| C23×C4×C3⋊D3 | 2 |
| C2×#63781 | 2 |
| C22×#95 | 9 |