Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
570 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 226 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #157 |
| commutator, hypocenter | C32 | C42×C8 |
| Frattini | C2×C4 | C22×#157 |
| Fitting | C32×C4×C8 | C4 |
| socle | C22×C32 | C2×C42 |
| prime radical | C22×C3⋊D3 | C22×C4 |
| cosocle | C2×C4×C3⋊D3 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C4×#622 | C4 | semidirect |
| 11. C8×#157 | C4 | direct (N × H) |
| 12. C32×C4×C8 | C4 | semidirect |
| 13. C8×C3⋊Dic3 | C4 | semidirect |
| 14. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 20. C4×#157 | C8 | direct (N × H) |
| 44. #622 | C42 | semidirect |
| 45. C32×C8 | C42 | semidirect |
| 46. C3⋊(C3⋊C8) | C42 | semidirect |
| 62. #157 | C4×C8 | direct (N × H) |
| 63. C32×C4 | C4×C8 | semidirect |
| 65. C3⋊Dic3 | C4×C8 | semidirect |
| 76. C4×C8 | #157 | direct (N × H) |
| 109. C32 | C42×C8 | semidirect |
| 121. C8 | C4×#157 | direct (N × H) |
| 131. C4 | C8×#157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#157 | 2 |
| C42×#157 | 2 |
| C4×#3787 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C42×C8 | 9 |