Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#22583629 | C2 | semidirect |
| 2. C2×#22583616 | C2 | semidirect |
| 3. #31827044 | C2 | semidirect |
| 4. #31826710 | C2 | semidirect |
| 5. #31826709 | C2 | semidirect |
| 6. #31826707 | C2 | semidirect |
| 7. #31826706 | C2 | semidirect |
| 8. #31826698 | C2 | semidirect |
| 9. #107×D283 | C2 | semidirect |
| 10. #31826463 | C2 | semidirect |
| 11. #466×C283 | C2 | semidirect |
| 64. C8×D283 | D4 | semidirect |
| 143. C283 | #3061 | semidirect |
| 153. #466 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583629 | 2 |
| C2×#22583616 | 2 |
| #31827044 | 2 |
| #31826710 | 2 |
| #31826709 | 2 |
| #31826707 | 2 |
| #31826706 | 2 |
| #31826698 | 2 |
| #107×D283 | 2 |
| #31826463 | 2 |
| #466×C283 | 2 |
| #3061 | 283 |