Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10593265 | C2 | direct (N × H) |
| 28. C2×C3⋊Dic3 | C16 | semidirect |
| 52. C3⋊Dic3 | C2×C16 | semidirect |
| 71. C2×C32 | C4⋊C16 | semidirect |
| 96. C32 | C2×C4⋊C16 | semidirect |
| 124. C2 | #10593265 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3771 | 2 |
| C2×C4×#622 | 2 |
| #10593265 | 2 |
| C2×C4⋊C16 | 9 |