Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
714 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 4. #10593395 | C2 | direct (N × H) |
| 21. C2×#622 | Q8 | semidirect |
| 47. #622 | C2×Q8 | semidirect |
| 96. C2×C32 | #500 | semidirect |
| 123. C32 | C2×#500 | semidirect |
| 150. C2 | #10593395 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63919 | 2 |
| C2×C4×#622 | 2 |
| C2×#63743 | 2 |
| #10593395 | 2 |
| C2×#500 | 9 |