Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31826835 | C2 | semidirect |
| 3. #31826827 | C2 | semidirect |
| 4. #31826822 | C2 | semidirect |
| 5. #31826817 | C2 | semidirect |
| 6. #31826473 | C2 | semidirect |
| 9. C2×#22583533 | C2 | semidirect |
| 10. #31826421 | C2 | semidirect |
| 11. #544×C283 | C2 | semidirect |
| 127. C283 | #3137 | semidirect |
| 129. #544 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827041 | 2 |
| #31826835 | 2 |
| #31826827 | 2 |
| #31826822 | 2 |
| #31826817 | 2 |
| #31826473 | 2 |
| #31826464 | 2 |
| #31826459 | 2 |
| C2×#22583533 | 2 |
| #31826421 | 2 |
| #544×C283 | 2 |
| #3137 | 283 |