Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
828 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 230 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 |
|---|---|---|
| 5. #10588863 | C2 | direct (N × H) |
| 79. C2×Dic9 | Q16 | semidirect |
| 122. Dic9 | C2×Q16 | semidirect |
| 157. C2×C9 | #494 | semidirect |
| 191. C9 | C2×#494 | semidirect |
| 224. C2 | #10588863 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Q16 | 2 |
| C2×#63506 | 2 |
| C22×#3674 | 2 |
| C22×Dic36 | 2 |
| #10588863 | 2 |
| C2×C8×Dic9 | 2 |
| C2×#5183 | 3 |