Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22583640 | C2 | semidirect |
| 3. C22×#17985381 | C2 | semidirect |
| 4. #31826728 | C2 | direct (N × H) |
| 5. C2×#22583546 | C2 | semidirect |
| 6. C2×#22583528 | C2 | semidirect |
| 7. C2×#22583526 | C2 | semidirect |
| 8. C2×#131×C283 | C2 | semidirect |
| 12. #22583640 | C22 | semidirect |
| 19. C2×#17985381 | C22 | semidirect |
| 25. #22583546 | C22 | semidirect |
| 26. #22583528 | C22 | semidirect |
| 27. #22583526 | C22 | semidirect |
| 30. #131×C283 | C22 | semidirect |
| 135. C2×C283 | #471 | semidirect |
| 138. C283 | C2×#471 | semidirect |
| 143. C2×#131 | D283 | semidirect |
| 164. #131 | C2×D283 | semidirect |
| 275. C2 | #31826728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583640 | 2 |
| C2×#22583635 | 2 |
| C22×#17985381 | 2 |
| #31826728 | 2 |
| C2×#22583546 | 2 |
| C2×#22583528 | 2 |
| C2×#22583526 | 2 |
| C2×#131×C283 | 2 |
| C2×#471 | 283 |