Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
153 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 153 conjugacy classes of subgroups — too many to draw. Only its 98 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. C4⋊(C3⋊C32) | C3 | direct (N × H) |
| 60. C32×C4 | C32 | semidirect |
| 103. C3×C4 | C3⋊C32 | semidirect |
| 104. C3×C4 | C3×C32 | semidirect |
| 109. C32 | C4⋊C32 | semidirect |
| 127. C4 | C3×C3⋊C32 | semidirect |
| 131. C3 | C4⋊(C3⋊C32) | direct (N × H) |
| 132. C3 | C3×C4⋊C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×C16 | 2 |
| C2×C3×C3⋊C32 | 2 |
| C3×C4⋊C32 | 3 |
| C4⋊(C3⋊C32) | 3 |