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. #10590900 | C2 | direct (N × H) |
| 30. C2×C32×C8 | Q8 | semidirect |
| 34. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 67. C32×C8 | C2×Q8 | semidirect |
| 68. C3⋊(C3⋊C8) | C2×Q8 | semidirect |
| 84. C2×C3×C8 | Dic6 | semidirect |
| 138. C3×C8 | C2×Dic6 | semidirect |
| 141. C2×C32 | #498 | semidirect |
| 151. C2×C8 | #627 | semidirect |
| 174. C32 | C2×#498 | semidirect |
| 186. C8 | C2×#627 | semidirect |
| 190. C2×C3 | #4855 | semidirect |
| 202. C3 | C2×#4855 | semidirect |
| 203. C2 | #10590900 | 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×#817 | 2 |
| C2×#63574 | 2 |
| #10590900 | 2 |
| C2×#4855 | 3 |