Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
4121 conjugacy classes of subgroups; only the 1188 normal subgroups are shown.
This group has 4121 conjugacy classes of subgroups — too many to draw. Only its 1188 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×C3×C3⋊C8 | C2 | semidirect |
| 3. C22×#3712 | C2 | direct (N × H) |
| 10. C22×C3×C3⋊C8 | C22 | semidirect |
| 11. C2×#3712 | C22 | direct (N × H) |
| 15. C23×C3⋊C8 | D3 | semidirect |
| 25. C2×C3×C3⋊C8 | C23 | semidirect |
| 26. #3712 | C23 | direct (N × H) |
| 39. C22×C3⋊C8 | C2×D3 | semidirect |
| 41. C23×C32 | M16 | semidirect |
| 50. C3×C3⋊C8 | C24 | semidirect |
| 71. C2×C3⋊C8 | C22×D3 | semidirect |
| 73. C22×C32 | C2×M16 | semidirect |
| 89. C23×C3 | ΓL(1,𝔽25) | semidirect |
| 106. C3⋊C8 | C23×D3 | semidirect |
| 107. C2×C32 | C22×M16 | semidirect |
| 122. C22×C3 | C2×ΓL(1,𝔽25) | semidirect |
| 134. C32 | C23×M16 | semidirect |
| 137. C23 | #3712 | direct (N × H) |
| 147. C2×C3 | C22×ΓL(1,𝔽25) | semidirect |
| 153. C22 | C2×#3712 | direct (N × H) |
| 159. C3 | C23×ΓL(1,𝔽25) | semidirect |
| 161. C2 | C22×#3712 | 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×#3712 | 2 |
| C23×ΓL(1,𝔽25) | 3 |