Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
250 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10593251 | C2 | semidirect |
| 4. C8×AGL(1,𝔽9) | C2 | semidirect |
| 18. C2×#622 | C8 | semidirect |
| 22. #3787 | C8 | semidirect |
| 25. C2×C32×C8 | C8 | semidirect |
| 26. C2×C3⋊(C3⋊C8) | C8 | semidirect |
| 27. C8×C3⋊D3 | C8 | semidirect |
| 28. C8×C3⋊D3 | C8 | semidirect |
| 108. C2×C8 | AGL(1,𝔽9) | semidirect |
| 120. C32 | #1450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596484 | 2 |
| C2×C8×#157 | 2 |
| #10593251 | 2 |
| C8×AGL(1,𝔽9) | 2 |
| #1450 | 9 |