Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
474 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 10. C4×#622 | C4 | semidirect |
| 11. #63742 | C4 | direct (N × H) |
| 46. #622 | C42 | semidirect |
| 66. C32×C4 | #106 | semidirect |
| 125. C32 | C4×#106 | semidirect |
| 154. C4 | #63742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#622 | 2 |
| C2×#63742 | 2 |
| C4×#3724 | 2 |
| #10590075 | 2 |
| C4×#106 | 9 |