Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 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×#22583658 | C2 | semidirect |
| 2. C2×#22583630 | C2 | semidirect |
| 3. #31827043 | C2 | semidirect |
| 4. #31826626 | C2 | semidirect |
| 5. #31826619 | C2 | semidirect |
| 6. #31826609 | C2 | semidirect |
| 7. #31826602 | C2 | semidirect |
| 8. #31826467 | C2 | semidirect |
| 9. C2×#22583534 | C2 | semidirect |
| 10. #31826433 | C2 | semidirect |
| 11. C2×#137×C283 | C2 | semidirect |
| 52. #17985392 | D4 | semidirect |
| 86. C2×Q8×C283 | D4 | semidirect |
| 169. C283 | #3013 | semidirect |
| 172. C2×#137 | D283 | semidirect |
| 233. C2×Q8 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583658 | 2 |
| C2×#22583630 | 2 |
| #31827043 | 2 |
| #31826626 | 2 |
| #31826619 | 2 |
| #31826609 | 2 |
| #31826602 | 2 |
| #31826467 | 2 |
| C2×#22583534 | 2 |
| #31826433 | 2 |
| C2×#137×C283 | 2 |
| #3013 | 283 |