Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
225 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 4. #10588863 | C2 | semidirect |
| 5. #10588242 | C2 | semidirect |
| 6. #10588195 | C2 | semidirect |
| 7. #10588188 | C2 | semidirect |
| 185. C9 | #2214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#510 | 2 |
| #10588876 | 2 |
| #10588875 | 2 |
| #10588863 | 2 |
| #10588242 | 2 |
| #10588195 | 2 |
| #10588188 | 2 |
| #71520 | 3 |