Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 1. #31827198 | C2 | semidirect |
| 2. #31826849 | C2 | semidirect |
| 3. #31826848 | C2 | semidirect |
| 5. #31826680 | C2 | semidirect |
| 6. #31826679 | C2 | semidirect |
| 7. #31826664 | C2 | semidirect |
| 8. C8×Dic566 | C2 | semidirect |
| 9. #31826559 | C2 | semidirect |
| 10. #31826547 | C2 | semidirect |
| 11. C4×D8×C283 | C2 | semidirect |
| 120. C283 | #3396 | semidirect |
| 132. C4×D8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827198 | 2 |
| #31826849 | 2 |
| #31826848 | 2 |
| #31826840 | 2 |
| #31826680 | 2 |
| #31826679 | 2 |
| #31826664 | 2 |
| C8×Dic566 | 2 |
| #31826559 | 2 |
| #31826547 | 2 |
| C4×D8×C283 | 2 |
| #3396 | 283 |