Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#22583617 | C2 | semidirect |
| 2. #31826587 | C2 | semidirect |
| 3. #31826582 | C2 | semidirect |
| 4. #31826514 | C2 | semidirect |
| 5. #31826482 | C2 | semidirect |
| 6. #31826423 | C2 | semidirect |
| 10. #22583617 | C22 | semidirect |
| 11. #22583617 | C22 | semidirect |
| 17. #22583546 | C22 | semidirect |
| 18. #22583537 | C22 | semidirect |
| 19. #22583520 | C22 | semidirect |
| 20. C8×Dic283 | C22 | semidirect |
| 22. #137×C283 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C283 | C4 | semidirect |
| 89. C283 | #2955 | semidirect |
| 99. #137 | Dic283 | semidirect |
| 100. AGL(1,ℤ/8) | Dic283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583617 | 2 |
| #31826587 | 2 |
| #31826582 | 2 |
| #31826514 | 2 |
| #31826482 | 2 |
| #31826423 | 2 |
| #575×C283 | 2 |
| #2955 | 283 |