Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
| 3. C2×#22583610 | C2 | semidirect |
| 4. #31826860 | C2 | direct (N × H) |
| 5. C2×#22583521 | C2 | semidirect |
| 9. C2×#17985382 | C22 | semidirect |
| 14. #22583610 | C22 | semidirect |
| 16. #22583521 | C22 | semidirect |
| 79. C2×C283 | #497 | semidirect |
| 82. C283 | C2×#497 | semidirect |
| 162. C2 | #31826860 | 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×#17985380 | 2 |
| C2×#22583610 | 2 |
| #31826860 | 2 |
| C2×#22583521 | 2 |
| C2×#124×C283 | 2 |
| C2×#497 | 283 |