Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
642 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 1. C32×#498 | C2 | semidirect |
| 3. #10592779 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 16. C3×#498 | D3 | semidirect |
| 52. C32×C8 | SD16 | semidirect |
| 53. C3⋊(C3⋊C8) | SD16 | semidirect |
| 55. #498 | C3⋊D3 | semidirect |
| 96. C3×C8 | #215 | semidirect |
| 120. C32 | #1705 | semidirect |
| 131. C8 | #3755 | semidirect |
| 142. C3 | #71332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#498 | 2 |
| #10592784 | 2 |
| #10592779 | 2 |
| #10592392 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #71332 | 3 |