Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
636 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 3. C32×C82 | C2 | semidirect |
| 4. #10589320 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 18. C3×C82 | D3 | semidirect |
| 30. C8×C3⋊D3 | C8 | semidirect |
| 56. C82 | C3⋊D3 | semidirect |
| 114. C32 | #1450 | semidirect |
| 136. C3 | #68047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592384 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C32×C82 | 2 |
| #10589320 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #68047 | 3 |