Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
318 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C2×C82 |
| Frattini | C4 | C22×AGL(1,𝔽9) |
| Fitting | C2×C32×C8 | C8 |
| socle | C22×C32 | C4×C8 |
| prime radical | C22×C3⋊D3 | C42 |
| cosocle | C4×#157 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C8×AGL(1,𝔽9) | C2 | direct (N × H) |
| 13. C2×AGL(1,𝔽9) | C8 | direct (N × H) |
| 16. C2×#622 | C8 | semidirect |
| 20. #3787 | C8 | semidirect |
| 22. C2×C32×C8 | C8 | semidirect |
| 23. C2×C3⋊(C3⋊C8) | C8 | semidirect |
| 24. C8×C3⋊D3 | C8 | semidirect |
| 32. AGL(1,𝔽9) | C2×C8 | direct (N × H) |
| 39. #622 | C2×C8 | semidirect |
| 40. C32×C8 | C2×C8 | semidirect |
| 41. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 77. C2×C32 | C82 | semidirect |
| 79. C3⋊D3 | C82 | semidirect |
| 91. C2×C8 | AGL(1,𝔽9) | direct (N × H) |
| 103. C32 | C2×C82 | semidirect |
| 117. C8 | C2×AGL(1,𝔽9) | direct (N × H) |
| 135. C2 | C8×AGL(1,𝔽9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×AGL(1,𝔽9) | 2 |
| C2×C8×#157 | 2 |
| C8×AGL(1,𝔽9) | 2 |
| C2×C82 | 9 |