Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
513 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 8. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 120. C32 | #1835 | semidirect |
| 145. C3 | #69547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C3×#4936 | 2 |
| #10589163 | 2 |
| #69547 | 3 |