Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31827093 | C2 | semidirect |
| 3. #31826830 | C2 | semidirect |
| 4. #31826825 | C2 | semidirect |
| 5. #31826820 | C2 | semidirect |
| 6. #31826812 | C2 | semidirect |
| 7. #31826471 | C2 | semidirect |
| 8. #31826467 | C2 | semidirect |
| 9. #31826462 | C2 | semidirect |
| 10. C2×#22583532 | C2 | semidirect |
| 11. #405×C283 | C2 | semidirect |
| 14. #22583610 | C22 | semidirect |
| 17. #22583602 | C22 | semidirect |
| 26. #22583535 | C22 | semidirect |
| 27. #22583535 | C22 | semidirect |
| 28. #22583535 | C22 | semidirect |
| 33. #22583532 | C22 | semidirect |
| 34. #22583532 | C22 | semidirect |
| 35. #22583532 | C22 | semidirect |
| 39. #97×C283 | C22 | semidirect |
| 40. C4×C8×C283 | C22 | semidirect |
| 135. C283 | #3136 | semidirect |
| 147. #405 | D283 | semidirect |
| 175. #97 | C2×D283 | semidirect |
| 176. C4×C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827093 | 2 |
| #31827034 | 2 |
| #31826830 | 2 |
| #31826825 | 2 |
| #31826820 | 2 |
| #31826812 | 2 |
| #31826471 | 2 |
| #31826467 | 2 |
| #31826462 | 2 |
| C2×#22583532 | 2 |
| #405×C283 | 2 |
| #3136 | 283 |