Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #28408935 | C2 | semidirect |
| 3. #28408932 | C2 | semidirect |
| 4. #28408926 | C2 | semidirect |
| 5. #28408924 | C2 | semidirect |
| 6. #28408921 | C2 | semidirect |
| 7. #28408911 | C2 | semidirect |
| 8. #28408887 | C2 | semidirect |
| 9. #386×C227 | C2 | semidirect |
| 12. #20300256 | C4 | semidirect |
| 13. C2×C4⋊Dic227 | C22 | semidirect |
| 14. C2×Dic227⋊C4 | C22 | semidirect |
| 17. C2×C22⋊Dic227 | C22 | semidirect |
| 23. C2×C4×Dic227 | C22 | semidirect |
| 24. C2×C4×Dic227 | C22 | semidirect |
| 25. C227⋊#95 | C22 | semidirect |
| 26. C227⋊#95 | C22 | semidirect |
| 28. C23×C4×C227 | C22 | semidirect |
| 30. C2×C22⋊C4×C227 | C22 | semidirect |
| 31. #95×C227 | C22 | semidirect |
| 36. C23×D227 | C2×C4 | semidirect |
| 48. C22⋊Dic227 | C2×C4 | semidirect |
| 53. (C2×D227)⋊C4 | C2×C4 | semidirect |
| 149. C227 | #2375 | semidirect |
| 158. #386 | D227 | semidirect |
| 163. C23×C4 | C2×D227 | semidirect |
| 176. C2×C22⋊C4 | C2×D227 | semidirect |
| 181. #95 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300256 | 2 |
| #28408935 | 2 |
| #28408932 | 2 |
| #28408926 | 2 |
| #28408924 | 2 |
| #28408921 | 2 |
| #28408911 | 2 |
| #28408887 | 2 |
| #386×C227 | 2 |
| #2375 | 227 |