Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #28409507 | C2 | semidirect |
| 3. #28409506 | C2 | semidirect |
| 4. #28409141 | C2 | semidirect |
| 5. #28409112 | C2 | semidirect |
| 6. #28409068 | C2 | semidirect |
| 7. #28409038 | C2 | semidirect |
| 8. #28408990 | C2 | semidirect |
| 9. #418×C227 | C2 | semidirect |
| 11. C2×#16813869 | C4 | semidirect |
| 17. D4×Dic227 | C22 | semidirect |
| 18. #20300250 | C22 | semidirect |
| 23. #20300221 | C22 | semidirect |
| 24. #20300219 | C22 | semidirect |
| 25. #20300210 | C22 | semidirect |
| 26. #20300198 | C22 | semidirect |
| 27. C8×Dic227 | C22 | semidirect |
| 31. #102×C227 | C22 | semidirect |
| 35. C2×D908 | C2×C4 | semidirect |
| 39. #16813869 | C2×C4 | semidirect |
| 40. #16813869 | C2×C4 | semidirect |
| 41. C2×C227⋊C8 | C2×C4 | semidirect |
| 55. C2×D4×C227 | C2×C4 | semidirect |
| 108. C227 | #2948 | semidirect |
| 117. #418 | D227 | semidirect |
| 138. #102 | C2×D227 | semidirect |
| 149. C2×D4 | C4×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813869 | 2 |
| #28409507 | 2 |
| #28409506 | 2 |
| #28409141 | 2 |
| #28409112 | 2 |
| #28409068 | 2 |
| #28409038 | 2 |
| #28408990 | 2 |
| #418×C227 | 2 |
| #2948 | 227 |