Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #31827190 | C2 | semidirect |
| 3. #31826818 | C2 | semidirect |
| 4. #31826763 | C2 | semidirect |
| 5. #31826747 | C2 | semidirect |
| 6. #31826686 | C2 | semidirect |
| 8. C8×Dic566 | C2 | semidirect |
| 9. C4×Dic1132 | C2 | semidirect |
| 10. #31826556 | C2 | semidirect |
| 117. C283 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827201 | 2 |
| #31827190 | 2 |
| #31826818 | 2 |
| #31826763 | 2 |
| #31826747 | 2 |
| #31826686 | 2 |
| #31826662 | 2 |
| C8×Dic566 | 2 |
| C4×Dic1132 | 2 |
| #31826556 | 2 |
| #486×C283 | 2 |
| #3365 | 283 |