Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
758 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 287 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×#63744 | C2 | direct (N × H) |
| 12. #63744 | C22 | direct (N × H) |
| 15. C22×#157 | C8 | semidirect |
| 37. C2×#157 | C2×C8 | semidirect |
| 60. C22×C32 | C4⋊C8 | semidirect |
| 62. C2×C3⋊D3 | C4⋊C8 | semidirect |
| 68. #157 | C22×C8 | semidirect |
| 96. C2×C32 | C2×C4⋊C8 | semidirect |
| 98. C3⋊D3 | C2×C4⋊C8 | semidirect |
| 128. C32 | C22×C4⋊C8 | semidirect |
| 158. C22 | #63744 | direct (N × H) |
| 170. C2 | C2×#63744 | 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×#3787 | 2 |
| C2×#63744 | 2 |
| C22×C4⋊C8 | 9 |