Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31826795 | C2 | semidirect |
| 5. #31826508 | C2 | semidirect |
| 6. #31826473 | C2 | semidirect |
| 18. #22583543 | C22 | semidirect |
| 19. #22583541 | C22 | semidirect |
| 20. #22583533 | C22 | semidirect |
| 21. #22583533 | C22 | semidirect |
| 116. C283 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583589 | 2 |
| #31826806 | 2 |
| #31826800 | 2 |
| #31826795 | 2 |
| #31826508 | 2 |
| #31826473 | 2 |
| #31826429 | 2 |
| C2×#117×C283 | 2 |
| #3095 | 283 |