Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
234 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 118 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. #10588167 | C2 | semidirect |
| 5. #10588166 | C2 | semidirect |
| 15. #63371 | C4 | semidirect |
| 34. C9⋊C16 | C2×C4 | semidirect |
| 135. C9 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#427 | 2 |
| C2×#63378 | 2 |
| C2×#63371 | 2 |
| #10588167 | 2 |
| #10588166 | 2 |
| #70649 | 3 |