Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
222 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 87 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. #10590082 | C2 | direct (N × H) |
| 31. C2×#157 | C16 | semidirect |
| 61. #157 | C2×C16 | semidirect |
| 85. C2×C32 | C4⋊C16 | semidirect |
| 87. C3⋊D3 | C4⋊C16 | semidirect |
| 114. C32 | C2×C4⋊C16 | semidirect |
| 151. C2 | #10590082 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#157 | 2 |
| C2×#63764 | 2 |
| #10590082 | 2 |
| C2×C4⋊C16 | 9 |