Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
314 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 23. C32×C42 | C8 | semidirect |
| 24. C4×C3⋊Dic3 | C8 | semidirect |
| 25. C4×C3⋊Dic3 | C8 | semidirect |
| 102. C42 | AGL(1,𝔽9) | semidirect |
| 112. C32 | #1831 | 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 |
| C42×#157 | 2 |
| #10593267 | 2 |
| #1831 | 9 |