Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#20300741 | C2 | semidirect |
| 2. #28410583 | C2 | semidirect |
| 3. #28410582 | C2 | semidirect |
| 4. #28410578 | C2 | semidirect |
| 5. #28410577 | C2 | semidirect |
| 6. #28410572 | C2 | semidirect |
| 7. C2×#20300725 | C2 | semidirect |
| 8. C2×#41×C457 | C2 | semidirect |
| 12. #20300741 | C22 | semidirect |
| 13. C2×Dic914 | C22 | semidirect |
| 14. C2×D1828 | C22 | semidirect |
| 17. #20300731 | C22 | semidirect |
| 18. #20300729 | C22 | semidirect |
| 19. #20300728 | C22 | semidirect |
| 20. #20300726 | C22 | semidirect |
| 21. #20300725 | C22 | semidirect |
| 22. #20300725 | C22 | semidirect |
| 23. C2×#16814532 | C22 | semidirect |
| 27. #41×C457 | C22 | semidirect |
| 28. C2×Q8×C457 | C22 | semidirect |
| 30. C2×D4×C457 | C22 | semidirect |
| 81. C457 | #575 | semidirect |
| 84. C2×#41 | D457 | semidirect |
| 98. #41 | C2×D457 | semidirect |
| 100. C2×Q8 | C2×D457 | semidirect |
| 104. C2×D4 | C2×D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300741 | 2 |
| #28410583 | 2 |
| #28410582 | 2 |
| #28410578 | 2 |
| #28410577 | 2 |
| #28410572 | 2 |
| C2×#20300725 | 2 |
| C2×#41×C457 | 2 |
| #575 | 457 |