Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
446 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#22583643 | C2 | semidirect |
| 3. C2×#22583640 | C2 | semidirect |
| 4. #31826740 | C2 | semidirect |
| 5. #31826728 | C2 | semidirect |
| 6. #31826514 | C2 | semidirect |
| 7. #31826447 | C2 | semidirect |
| 8. C2×#22583528 | C2 | semidirect |
| 9. #568×C283 | C2 | semidirect |
| 21. C2×Dic1132 | C22 | semidirect |
| 23. C2×#17985381 | C22 | semidirect |
| 27. #22583546 | C22 | semidirect |
| 28. #22583528 | C22 | semidirect |
| 29. #22583528 | C22 | semidirect |
| 30. #22583526 | C22 | semidirect |
| 142. C283 | #3069 | semidirect |
| 147. #568 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827263 | 2 |
| C2×#22583643 | 2 |
| C2×#22583640 | 2 |
| #31826740 | 2 |
| #31826728 | 2 |
| #31826514 | 2 |
| #31826447 | 2 |
| C2×#22583528 | 2 |
| #568×C283 | 2 |
| #3069 | 283 |