Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
264 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C9 | #121 |
| commutator | C22×C4 | C23×C9 |
| Frattini, cosocle | C22×C3×C4 | C23×C3 |
| socle | C22×C3 | C3×#121 |
| prime radical | C23×C3 | C3×#41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C22×C4×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 36. #2089 | C9 | direct (N × H) |
| 138. C9 | #2089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#428 | 2 |
| C2×C9×#107 | 2 |
| C9×#424 | 2 |
| C9×#343 | 2 |
| C9×#341 | 2 |
| C3×#2089 | 3 |