Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 36. C32×C4⋊C4 | C8 | semidirect |
| 37. C4⋊(C3⋊Dic3) | C8 | semidirect |
| 38. #3750 | C8 | semidirect |
| 89. C32×C4 | C4⋊C8 | semidirect |
| 91. C3⋊Dic3 | C4⋊C8 | semidirect |
| 136. C4⋊C4 | AGL(1,𝔽9) | semidirect |
| 152. C32 | #1939 | semidirect |
| 200. C4 | C4⋊AGL(1,𝔽9) | semidirect |
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×C4×AGL(1,𝔽9) | 2 |
| C4⋊C4×#157 | 2 |
| #10593267 | 2 |
| #1939 | 9 |