Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
270 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C2×C4×C16 |
| Frattini | C22 | C22×AGL(1,𝔽9) |
| Fitting | C32×C42 | C8 |
| socle | C22×C32 | C22×C8 |
| prime radical | C22×C3⋊D3 | C2×C8 |
| cosocle | C2×#622 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×#3771 | C2 | semidirect |
| 7. #64213 | C4 | direct (N × H) |
| 18. #3771 | C2×C4 | semidirect |
| 29. C4×C3⋊D3 | C16 | semidirect |
| 47. C32×C4 | C2×C16 | semidirect |
| 48. C3⋊Dic3 | C2×C16 | semidirect |
| 68. C3⋊D3 | C4×C16 | semidirect |
| 88. C32 | C2×C4×C16 | semidirect |
| 109. C4 | #64213 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64213 | 2 |
| C4×#3787 | 2 |
| C4×#3771 | 2 |
| C2×C4×C16 | 9 |