Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
339 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. C22×Dic36 | C2 | semidirect |
| 3. C2×#63386 | C2 | semidirect |
| 4. #10588226 | C2 | semidirect |
| 5. #10588169 | C2 | semidirect |
| 39. Dic36 | D4 | semidirect |
| 98. C22×C9 | SD32 | semidirect |
| 168. C9 | #2185 | semidirect |
| 196. C22 | #63386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic36 | 2 |
| C9×#466 | 2 |
| C2×#63386 | 2 |
| #10588226 | 2 |
| #10588169 | 2 |
| #71077 | 3 |