Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1224 conjugacy classes of subgroups; only the 609 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 609 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×C4×C8 | C3⋊D3 |
| commutator, hypocenter | C32 | C42×C8 |
| Frattini | C22×C4 | C22×C3⋊D3 |
| Fitting | C2×C32×C4×C8 | C2 |
| socle, prime radical | C23×C32 | C22×C4 |
| cosocle | C22×C32×C4 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C32×C4×C8 | C4 | semidirect |
| 12. C8×C3⋊Dic3 | C4 | direct (N × H) |
| 13. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 25. C4×C3⋊Dic3 | C8 | direct (N × H) |
| 35. C3×C4×C8 | Dic3 | semidirect |
| 46. C32×C8 | C42 | semidirect |
| 47. C3⋊(C3⋊C8) | C42 | semidirect |
| 66. C32×C4 | C4×C8 | semidirect |
| 69. C3⋊Dic3 | C4×C8 | direct (N × H) |
| 77. C4×C8 | C3⋊Dic3 | direct (N × H) |
| 86. C3×C8 | C4×Dic3 | semidirect |
| 105. C3×C4 | C8×Dic3 | semidirect |
| 109. C32 | C42×C8 | semidirect |
| 119. C8 | C4×C3⋊Dic3 | direct (N × H) |
| 127. C4 | C8×C3⋊Dic3 | direct (N × H) |
| 130. C3 | C4×C8×Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×C8 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C42×C3⋊Dic3 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C4×C8×Dic3 | 3 |