Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3338 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 3338 conjugacy classes of subgroups — too many to draw. Only its 1106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #157 |
| commutator, hypocenter | C32 | C24×C8 |
| Frattini | C2 | C24×#157 |
| Fitting | C23×C32×C4 | C4 |
| socle | C24×C32 | C2×C4 |
| prime radical | C24×C3⋊D3 | C4 |
| cosocle | C3⋊Dic3 | C25 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#622 | C2 | semidirect |
| 3. C22×#3787 | C2 | direct (N × H) |
| 9. C22×#622 | C22 | semidirect |
| 10. C2×#3787 | C22 | direct (N × H) |
| 13. C23×C3⋊D3 | C8 | semidirect |
| 20. C2×#622 | C23 | semidirect |
| 21. #3787 | C23 | direct (N × H) |
| 28. C23×C32 | C2×C8 | semidirect |
| 30. C22×C3⋊D3 | C2×C8 | semidirect |
| 37. #622 | C24 | semidirect |
| 49. C22×C32 | C22×C8 | semidirect |
| 51. C2×C3⋊D3 | C22×C8 | semidirect |
| 72. C2×C32 | C23×C8 | semidirect |
| 74. C3⋊D3 | C23×C8 | semidirect |
| 92. C32 | C24×C8 | semidirect |
| 95. C23 | #3787 | direct (N × H) |
| 108. C22 | C2×#3787 | direct (N × H) |
| 115. C2 | C22×#3787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C3⋊D3 | 2 |
| C23×#622 | 2 |
| C22×#3787 | 2 |
| C24×C8 | 9 |