Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #31826873 | C2 | semidirect |
| 4. #31826872 | C2 | semidirect |
| 5. #31826866 | C2 | semidirect |
| 6. #31826865 | C2 | semidirect |
| 48. #17985376 | Q8 | semidirect |
| 72. M16×C283 | Q8 | semidirect |
| 124. C283 | #3166 | semidirect |
| 176. M16 | Dic566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827018 | 2 |
| C2×#22583601 | 2 |
| #31826873 | 2 |
| #31826872 | 2 |
| #31826866 | 2 |
| #31826865 | 2 |
| #31826508 | 2 |
| #31826507 | 2 |
| #31826505 | 2 |
| M16×Dic283 | 2 |
| #428×C283 | 2 |
| #3166 | 283 |