Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
929 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 929 conjugacy classes of subgroups — too many to draw. Only its 268 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 |
|---|---|---|
| 5. #10590902 | C2 | direct (N × H) |
| 31. C2×C32×C8 | Q8 | semidirect |
| 35. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 70. C32×C8 | C2×Q8 | semidirect |
| 71. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 89. C2×C3×C8 | Dic6 | semidirect |
| 149. C3×C8 | C2×Dic6 | semidirect |
| 152. C2×C32 | #500 | semidirect |
| 164. C2×C8 | #627 | semidirect |
| 191. C32 | C2×#500 | semidirect |
| 205. C8 | C2×#627 | semidirect |
| 210. C2×C3 | #4874 | semidirect |
| 225. C3 | C2×#4874 | semidirect |
| 226. C2 | #10590902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63919 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C2×C3×#818 | 2 |
| C2×#63576 | 2 |
| #10590902 | 2 |
| C2×#4874 | 3 |