Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
636 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 230 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 |
|---|---|---|
| 6. #10588535 | C2 | direct (N × H) |
| 33. C2×C8×C9 | Q8 | semidirect |
| 42. C2×C9⋊C8 | Q8 | semidirect |
| 70. C8×C9 | C2×Q8 | semidirect |
| 71. C9⋊C8 | C2×Q8 | semidirect |
| 131. C2×C9 | #498 | semidirect |
| 142. C2×C8 | Dic18 | semidirect |
| 160. C9 | C2×#498 | semidirect |
| 174. C8 | C2×Dic18 | semidirect |
| 188. C2 | #10588535 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63450 | 2 |
| C2×C9×#106 | 2 |
| C2×#63377 | 2 |
| C2×C8×Dic9 | 2 |
| C2×#63367 | 2 |
| #10588535 | 2 |
| C2×#4855 | 3 |