Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
411 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 411 conjugacy classes of subgroups — too many to draw. Only its 116 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. #10588215 | C2 | semidirect |
| 6. C22×Q8×C9 | C4 | semidirect |
| 10. C9×C22⋊Q8 | C4 | semidirect |
| 13. C2×C9×C4⋊C4 | C4 | semidirect |
| 135. C22×Q8 | Dic9 | semidirect |
| 140. C22⋊Q8 | Dic9 | semidirect |
| 143. C2×C4⋊C4 | Dic9 | semidirect |
| 223. C9 | #1511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C22⋊Q8 | 2 |
| #10588891 | 2 |
| #10588887 | 2 |
| #10588215 | 2 |
| #71689 | 3 |