Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
870 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 870 conjugacy classes of subgroups — too many to draw. Only its 247 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 |
|---|---|---|
| 6. C2×C4×#157 | C4 | semidirect |
| 7. #63747 | C4 | direct (N × H) |
| 28. C2×#157 | C42 | semidirect |
| 48. C32×C4 | #95 | semidirect |
| 49. C3⋊Dic3 | #95 | semidirect |
| 88. C32 | C4×#95 | semidirect |
| 116. C4 | #63747 | 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 |
| C2×#63747 | 2 |
| C4×#95 | 9 |