Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. #28409515 | C2 | semidirect |
| 3. #28409038 | C2 | semidirect |
| 4. #28409034 | C2 | semidirect |
| 5. #28409029 | C2 | semidirect |
| 6. C2×#20300210 | C2 | semidirect |
| 7. C2×#131×C227 | C2 | semidirect |
| 9. #20300334 | C4 | semidirect |
| 16. #20300247 | C22 | semidirect |
| 17. C2×C4⋊Dic227 | C22 | semidirect |
| 18. #20300213 | C22 | semidirect |
| 19. #20300213 | C22 | semidirect |
| 20. #20300210 | C22 | semidirect |
| 21. #20300210 | C22 | semidirect |
| 22. #20300210 | C22 | semidirect |
| 25. C2×M16×C227 | C22 | semidirect |
| 26. C22×C8×C227 | C22 | semidirect |
| 30. #16813884 | C2×C4 | semidirect |
| 34. C2×D908 | C2×C4 | semidirect |
| 97. C227 | #2897 | semidirect |
| 100. C2×#131 | D227 | semidirect |
| 114. C2×M16 | C2×D227 | semidirect |
| 115. C22×C8 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300334 | 2 |
| #28409515 | 2 |
| #28409038 | 2 |
| #28409034 | 2 |
| #28409029 | 2 |
| C2×#20300210 | 2 |
| C2×#131×C227 | 2 |
| #2897 | 227 |