Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1200 conjugacy classes of subgroups; only the 425 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 425 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. C22×C32×C16 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊C16) | C2 | semidirect |
| 4. C2×#63625 | C2 | direct (N × H) |
| 11. C2×C32×C16 | C22 | semidirect |
| 12. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 13. #63625 | C22 | direct (N × H) |
| 15. C22×C3×C16 | D3 | semidirect |
| 28. C32×C16 | C23 | semidirect |
| 29. C3⋊(C3⋊C16) | C23 | semidirect |
| 36. C2×C3×C16 | C2×D3 | semidirect |
| 53. C22×C16 | C3⋊D3 | semidirect |
| 64. C3×C16 | C22×D3 | semidirect |
| 66. C22×C32 | M32 | semidirect |
| 80. C2×C16 | C2×C3⋊D3 | semidirect |
| 92. C2×C32 | C2×M32 | semidirect |
| 106. C16 | C22×C3⋊D3 | semidirect |
| 107. C22×C3 | #798 | semidirect |
| 114. C32 | C22×M32 | semidirect |
| 126. C2×C3 | C2×#798 | semidirect |
| 131. C22 | #63625 | direct (N × H) |
| 136. C3 | C22×#798 | semidirect |
| 138. C2 | C2×#63625 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C3⋊D3 | 2 |
| C22×C32×C16 | 2 |
| C22×C3⋊(C3⋊C16) | 2 |
| C2×#63625 | 2 |
| C22×#798 | 3 |