Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
300 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #95 |
| commutator | C23 | C42×C9 |
| Frattini, cosocle | C23×C3×C4 | C22×C3 |
| socle | C22×C3 | C3×#95 |
| prime radical | C24×C3 | C2×C3×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ C23×C4×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×C9×M16 | C4 | semidirect |
| 13. C9×C22⋊C8 | C4 | semidirect |
| 33. #1305 | C9 | direct (N × H) |
| 104. C2×M16 | C4×C9 | semidirect |
| 110. C22⋊C8 | C4×C9 | semidirect |
| 174. C9 | #1305 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#407 | 2 |
| C9×#380 | 2 |
| C3×#1305 | 3 |