Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×Q16×D283 | C2 | semidirect |
| 3. #31826907 | C2 | direct (N × H) |
| 4. C2×#22583556 | C2 | semidirect |
| 5. C2×#22583555 | C2 | semidirect |
| 6. C2×#22583553 | C2 | semidirect |
| 7. C2×#22583549 | C2 | semidirect |
| 8. C2×Q32×C283 | C2 | semidirect |
| 16. Q16×D283 | C22 | semidirect |
| 20. #22583556 | C22 | semidirect |
| 21. #22583555 | C22 | semidirect |
| 22. #22583553 | C22 | semidirect |
| 23. #22583549 | C22 | semidirect |
| 27. Q32×C283 | C22 | semidirect |
| 93. C2×C283 | #510 | semidirect |
| 97. C283 | C2×#510 | semidirect |
| 103. C2×Q32 | D283 | semidirect |
| 121. Q32 | C2×D283 | semidirect |
| 193. C2 | #31826907 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583633 | 2 |
| C2×Q16×D283 | 2 |
| #31826907 | 2 |
| C2×#22583556 | 2 |
| C2×#22583555 | 2 |
| C2×#22583553 | 2 |
| C2×#22583549 | 2 |
| C2×Q32×C283 | 2 |
| C2×#510 | 283 |