Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
4633 conjugacy classes of subgroups; only the 1444 normal subgroups are shown.
This group has 4633 conjugacy classes of subgroups — too many to draw. Only its 1444 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 | D32 |
| commutator, hypocenter | C32 | C24×C8 |
| Frattini | C4 | C23×D32 |
| Fitting | C23×C32×C4 | C22 |
| socle | C24×C32 | C2×C4 |
| prime radical | C24×C3⋊D3 | C4 |
| cosocle | C32×C4 | 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×C3×C3⋊C8 | C2 | semidirect |
| 3. C22×#3710 | C2 | direct (N × H) |
| 10. C22×C3×C3⋊C8 | C22 | semidirect |
| 11. C2×#3710 | C22 | direct (N × H) |
| 15. C23×C3⋊C8 | D3 | semidirect |
| 18. C23×C3⋊D3 | C8 | semidirect |
| 25. C2×C3×C3⋊C8 | C23 | semidirect |
| 26. #3710 | C23 | direct (N × H) |
| 39. C22×C3⋊C8 | C2×D3 | semidirect |
| 41. C23×C32 | C2×C8 | semidirect |
| 43. C22×C3⋊D3 | C2×C8 | semidirect |
| 50. C3×C3⋊C8 | C24 | semidirect |
| 71. C2×C3⋊C8 | C22×D3 | semidirect |
| 73. C22×C32 | C22×C8 | semidirect |
| 75. C2×C3⋊D3 | C22×C8 | semidirect |
| 89. C23×C3 | D3×C8 | semidirect |
| 106. C3⋊C8 | C23×D3 | semidirect |
| 107. C2×C32 | C23×C8 | semidirect |
| 109. C3⋊D3 | C23×C8 | semidirect |
| 122. C22×C3 | C2×D3×C8 | semidirect |
| 134. C32 | C24×C8 | semidirect |
| 137. C23 | #3710 | direct (N × H) |
| 147. C2×C3 | C22×D3×C8 | semidirect |
| 153. C22 | C2×#3710 | direct (N × H) |
| 159. C3 | C23×D3×C8 | semidirect |
| 161. C2 | C22×#3710 | 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×C3×C3⋊C8 | 2 |
| C22×#3710 | 2 |
| C23×D3×C8 | 3 |