Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
243 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 16. #63362 | C4 | semidirect |
| 17. C4×C9⋊C8 | C4 | semidirect |
| 180. C9 | #1841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3667 | 2 |
| C9×#339 | 2 |
| C9⋊#338 | 2 |
| #10588232 | 2 |
| #10588210 | 2 |
| #10588209 | 2 |
| #10588201 | 2 |
| #68749 | 3 |