Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 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. C2×#22583635 | C2 | semidirect |
| 2. C2×#22583607 | C2 | semidirect |
| 3. #31826855 | C2 | semidirect |
| 4. #31826841 | C2 | semidirect |
| 5. #31826839 | C2 | semidirect |
| 6. C4×#17985376 | C2 | semidirect |
| 7. #532×C283 | C2 | semidirect |
| 11. C2×#17985379 | C22 | semidirect |
| 12. C2×#17985377 | C22 | semidirect |
| 17. #22583521 | C22 | semidirect |
| 18. C4×C283⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C283 | C22 | semidirect |
| 21. #127×C283 | C22 | semidirect |
| 22. #124×C283 | C22 | semidirect |
| 35. #17985376 | D4 | semidirect |
| 57. C283⋊C8 | C2×D4 | semidirect |
| 83. C4×C283 | AGL(1,ℤ/8) | semidirect |
| 90. C283 | #3151 | semidirect |
| 93. #532 | D283 | semidirect |
| 106. C4⋊Q8 | C2×D283 | semidirect |
| 110. #127 | C2×D283 | semidirect |
| 111. #124 | C2×D283 | semidirect |
| 174. C4 | #22583635 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583635 | 2 |
| C2×#22583607 | 2 |
| #31826855 | 2 |
| #31826841 | 2 |
| #31826839 | 2 |
| C4×#17985376 | 2 |
| #532×C283 | 2 |
| #3151 | 283 |