Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
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×#20297736 | C2 | semidirect |
| 2. #28385371 | C2 | semidirect |
| 3. #28385370 | C2 | semidirect |
| 4. #28385366 | C2 | semidirect |
| 5. #28385365 | C2 | semidirect |
| 6. #28385360 | C2 | semidirect |
| 7. C2×#20297720 | C2 | semidirect |
| 8. C2×#41×C449 | C2 | semidirect |
| 12. #20297736 | C22 | semidirect |
| 13. C2×Dic898 | C22 | semidirect |
| 14. C2×D1796 | C22 | semidirect |
| 17. #20297726 | C22 | semidirect |
| 18. #20297724 | C22 | semidirect |
| 19. #20297723 | C22 | semidirect |
| 20. #20297721 | C22 | semidirect |
| 21. #20297720 | C22 | semidirect |
| 22. #20297720 | C22 | semidirect |
| 23. C2×#16813311 | C22 | semidirect |
| 27. #41×C449 | C22 | semidirect |
| 28. C2×Q8×C449 | C22 | semidirect |
| 30. C2×D4×C449 | C22 | semidirect |
| 81. C449 | #575 | semidirect |
| 84. C2×#41 | D449 | semidirect |
| 98. #41 | C2×D449 | semidirect |
| 100. C2×Q8 | C2×D449 | semidirect |
| 104. C2×D4 | C2×D449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20297736 | 2 |
| #28385371 | 2 |
| #28385370 | 2 |
| #28385366 | 2 |
| #28385365 | 2 |
| #28385360 | 2 |
| C2×#20297720 | 2 |
| C2×#41×C449 | 2 |
| #575 | 449 |