Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
5160 conjugacy classes of subgroups; only the 1577 normal subgroups are shown.
This group has 5160 conjugacy classes of subgroups — too many to draw. Only its 1577 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C32×C8 | C2 | semidirect |
| 3. C23×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C22×#3743 | C2 | direct (N × H) |
| 11. C22×C32×C8 | C22 | semidirect |
| 12. C22×C3⋊(C3⋊C8) | C22 | semidirect |
| 13. C2×#3743 | C22 | direct (N × H) |
| 15. C23×C3×C8 | D3 | semidirect |
| 26. C2×C32×C8 | C23 | semidirect |
| 27. C2×C3⋊(C3⋊C8) | C23 | semidirect |
| 28. #3743 | C23 | direct (N × H) |
| 35. C22×C3×C8 | C2×D3 | semidirect |
| 38. C23×C32 | M16 | semidirect |
| 47. C32×C8 | C24 | semidirect |
| 48. C3⋊(C3⋊C8) | C24 | semidirect |
| 52. C23×C8 | C3⋊D3 | semidirect |
| 61. C2×C3×C8 | C22×D3 | semidirect |
| 64. C22×C32 | C2×M16 | semidirect |
| 78. C22×C8 | C2×C3⋊D3 | semidirect |
| 79. C23×C3 | ΓL(1,𝔽25) | semidirect |
| 88. C3×C8 | C23×D3 | semidirect |
| 90. C2×C32 | C22×M16 | semidirect |
| 103. C2×C8 | C22×C3⋊D3 | semidirect |
| 104. C22×C3 | C2×ΓL(1,𝔽25) | semidirect |
| 111. C32 | C23×M16 | semidirect |
| 114. C23 | #3743 | direct (N × H) |
| 122. C8 | C23×C3⋊D3 | semidirect |
| 123. C2×C3 | C22×ΓL(1,𝔽25) | semidirect |
| 128. C22 | C2×#3743 | direct (N × H) |
| 133. C3 | C23×ΓL(1,𝔽25) | semidirect |
| 135. C2 | C22×#3743 | 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×C32×C8 | 2 |
| C23×C3⋊(C3⋊C8) | 2 |
| C22×#3743 | 2 |
| C23×ΓL(1,𝔽25) | 3 |