Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
618 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 238 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 |
|---|---|---|
| 2. C2×C9×#97 | C2 | semidirect |
| 4. C2×Dic9⋊C8 | C2 | semidirect |
| 5. C2×C4×C9⋊C8 | C2 | semidirect |
| 6. #10588390 | C2 | direct (N × H) |
| 17. C9×#97 | C22 | semidirect |
| 19. Dic9⋊C8 | C22 | semidirect |
| 20. C4×C9⋊C8 | C22 | semidirect |
| 80. C2×#97 | D9 | semidirect |
| 122. #97 | C2×D9 | semidirect |
| 141. C2×C9 | #433 | semidirect |
| 174. C9 | C2×#433 | semidirect |
| 209. C2 | #10588390 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63434 | 2 |
| C2×C9×#97 | 2 |
| C2×(C2×D9)⋊C8 | 2 |
| C2×Dic9⋊C8 | 2 |
| C2×C4×C9⋊C8 | 2 |
| #10588390 | 2 |
| C2×#4709 | 3 |