Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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. #31826806 | C2 | semidirect |
| 3. #31826800 | C2 | semidirect |
| 4. #31826789 | C2 | semidirect |
| 5. #31826778 | C2 | semidirect |
| 6. #31826508 | C2 | semidirect |
| 7. C2×#22583543 | C2 | semidirect |
| 8. #31826464 | C2 | semidirect |
| 9. #31826459 | C2 | semidirect |
| 10. #31826432 | C2 | semidirect |
| 11. #520×C283 | C2 | semidirect |
| 133. C283 | #3098 | semidirect |
| 136. #520 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827043 | 2 |
| #31826806 | 2 |
| #31826800 | 2 |
| #31826789 | 2 |
| #31826778 | 2 |
| #31826508 | 2 |
| C2×#22583543 | 2 |
| #31826464 | 2 |
| #31826459 | 2 |
| #31826432 | 2 |
| #520×C283 | 2 |
| #3098 | 283 |