Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 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. #28409509 | C2 | semidirect |
| 4. #28409131 | C2 | semidirect |
| 5. #28409119 | C2 | semidirect |
| 6. #28409040 | C2 | semidirect |
| 8. #28408987 | C2 | semidirect |
| 9. #427×C227 | C2 | semidirect |
| 12. C2×#16813873 | C4 | semidirect |
| 17. #20300253 | C22 | semidirect |
| 23. #20300211 | C22 | semidirect |
| 25. #20300198 | C22 | semidirect |
| 26. C8×Dic227 | C22 | semidirect |
| 30. #107×C227 | C22 | semidirect |
| 31. #106×C227 | C22 | semidirect |
| 35. C2×Dic454 | C2×C4 | semidirect |
| 43. #16813873 | C2×C4 | semidirect |
| 44. #16813873 | C2×C4 | semidirect |
| 54. C2×C8×C227 | C2×C4 | semidirect |
| 103. C227 | #2949 | semidirect |
| 110. #427 | D227 | semidirect |
| 130. #107 | C2×D227 | semidirect |
| 131. #106 | C2×D227 | semidirect |
| 152. C2×C8 | C4×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813873 | 2 |
| #28409509 | 2 |
| #28409506 | 2 |
| #28409131 | 2 |
| #28409119 | 2 |
| #28409040 | 2 |
| #28409036 | 2 |
| #28408987 | 2 |
| #427×C227 | 2 |
| #2949 | 227 |