Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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 |
|---|---|---|
| 1. C2×#22583657 | C2 | semidirect |
| 2. #31827263 | C2 | semidirect |
| 3. #31827036 | C2 | semidirect |
| 4. #31826646 | C2 | semidirect |
| 5. #31826636 | C2 | semidirect |
| 6. #31826482 | C2 | semidirect |
| 7. #31826481 | C2 | semidirect |
| 8. C2×#22583528 | C2 | semidirect |
| 9. #575×C283 | C2 | semidirect |
| 21. #22583641 | C22 | semidirect |
| 23. #22583636 | C22 | semidirect |
| 27. #22583608 | C22 | semidirect |
| 28. #22583597 | C22 | semidirect |
| 32. #22583537 | C22 | semidirect |
| 33. #22583536 | C22 | semidirect |
| 34. #22583528 | C22 | semidirect |
| 38. #137×C283 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C283 | C22 | semidirect |
| 185. C283 | #3020 | semidirect |
| 189. #575 | D283 | semidirect |
| 212. #137 | C2×D283 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583657 | 2 |
| #31827263 | 2 |
| #31827036 | 2 |
| #31826646 | 2 |
| #31826636 | 2 |
| #31826482 | 2 |
| #31826481 | 2 |
| C2×#22583528 | 2 |
| #575×C283 | 2 |
| #3020 | 283 |