Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#17985382 | C2 | semidirect |
| 4. #31826721 | C2 | direct (N × H) |
| 5. C2×#22583541 | C2 | semidirect |
| 6. C2×#22583534 | C2 | semidirect |
| 7. C2×#22583533 | C2 | semidirect |
| 11. C2×#17985382 | C22 | semidirect |
| 21. #22583541 | C22 | semidirect |
| 22. #22583534 | C22 | semidirect |
| 23. #22583533 | C22 | semidirect |
| 111. C2×C283 | #470 | semidirect |
| 115. C283 | C2×#470 | semidirect |
| 227. C2 | #31826721 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985382 | 2 |
| C22×#17985376 | 2 |
| C2×#22583589 | 2 |
| #31826721 | 2 |
| C2×#22583541 | 2 |
| C2×#22583534 | 2 |
| C2×#22583533 | 2 |
| C2×C22⋊Q8×C283 | 2 |
| C2×#470 | 283 |