Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 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. #31827201 | C2 | semidirect |
| 2. #31827185 | C2 | semidirect |
| 3. #31826848 | C2 | semidirect |
| 4. #31826837 | C2 | semidirect |
| 5. #31826686 | C2 | semidirect |
| 6. #31826678 | C2 | semidirect |
| 7. #31826676 | C2 | semidirect |
| 8. #31826589 | C2 | semidirect |
| 9. #31826556 | C2 | semidirect |
| 10. C4×#17985380 | C2 | semidirect |
| 125. C283 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827201 | 2 |
| #31827185 | 2 |
| #31826848 | 2 |
| #31826837 | 2 |
| #31826686 | 2 |
| #31826678 | 2 |
| #31826676 | 2 |
| #31826589 | 2 |
| #31826556 | 2 |
| C4×#17985380 | 2 |
| #459×C283 | 2 |
| #3394 | 283 |