Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
189 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 189 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 36. C3⋊(C3⋊C8) | C16 | semidirect |
| 103. C32 | #1370 | semidirect |
| 126. C3 | #67555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C3⋊(C3⋊C8) | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #67555 | 3 |