Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
282 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 282 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. #10590022 | C2 | direct (N × H) |
| 36. C2×#157 | C16 | semidirect |
| 68. #157 | C2×C16 | semidirect |
| 92. C2×C32 | C4⋊C16 | semidirect |
| 94. C3⋊D3 | C4⋊C16 | semidirect |
| 121. C32 | C2×C4⋊C16 | semidirect |
| 158. C2 | #10590022 | 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×#63542 | 2 |
| #10590022 | 2 |
| C2×C4⋊C16 | 9 |