Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
286 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 119 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 | direct (N × H) |
| 16. C2×#622 | C8 | semidirect |
| 20. #3787 | C8 | semidirect |
| 22. C2×C32×C8 | C8 | semidirect |
| 23. C2×C3⋊(C3⋊C8) | C8 | semidirect |
| 24. C8×C3⋊D3 | C8 | semidirect |
| 39. #622 | C2×C8 | semidirect |
| 40. C32×C8 | C2×C8 | semidirect |
| 41. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 77. C2×C32 | #322 | semidirect |
| 79. C3⋊D3 | #322 | semidirect |
| 91. C2×C8 | AGL(1,𝔽9) | semidirect |
| 103. C32 | C2×#322 | semidirect |
| 117. C8 | C2×AGL(1,𝔽9) | semidirect |
| 135. C2 | #10593251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×AGL(1,𝔽9) | 2 |
| C2×C8×#157 | 2 |
| #10593251 | 2 |
| C2×#322 | 9 |