Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
162 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C9 | C22⋊C4 |
| commutator | C22 | C2×C9×C16 |
| Frattini, cosocle | C22×C3×C8 | C22×C3 |
| socle | C22×C3 | C3×C22⋊C8 |
| prime radical | C23×C3 | C2×C3×C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C9 ◁ C22×C8×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. #1322 | C9 | direct (N × H) |
| 34. C2×C4×C9 | C16 | semidirect |
| 103. C9 | #1322 | direct (N × H) |
| 111. C2×C4 | C9×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C4⋊C8 | 2 |
| C9×C22⋊C16 | 2 |
| C3×#1322 | 3 |