Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 1. C2×#22583633 | C2 | semidirect |
| 2. C2×#22583629 | C2 | semidirect |
| 3. #31826896 | C2 | direct (N × H) |
| 4. C2×#22583556 | C2 | semidirect |
| 5. C2×#22583555 | C2 | semidirect |
| 6. C2×#22583551 | C2 | semidirect |
| 7. C2×C16×D283 | C2 | semidirect |
| 8. C2×SD32×C283 | C2 | semidirect |
| 12. #22583633 | C22 | semidirect |
| 14. #22583629 | C22 | semidirect |
| 20. #22583556 | C22 | semidirect |
| 21. #22583555 | C22 | semidirect |
| 22. #22583551 | C22 | semidirect |
| 24. C16×D283 | C22 | semidirect |
| 27. SD32×C283 | C22 | semidirect |
| 95. C2×C283 | #508 | semidirect |
| 99. C283 | C2×#508 | semidirect |
| 106. C2×SD32 | D283 | semidirect |
| 124. SD32 | C2×D283 | semidirect |
| 197. C2 | #31826896 | 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×#22583629 | 2 |
| #31826896 | 2 |
| C2×#22583556 | 2 |
| C2×#22583555 | 2 |
| C2×#22583551 | 2 |
| C2×C16×D283 | 2 |
| C2×SD32×C283 | 2 |
| C2×#508 | 283 |