Finite Group DatabasebetaFinite Group DatabasebetaOrder 28352.
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×#20296787 | C2 | semidirect |
| 2. #28381917 | C2 | semidirect |
| 3. #28381916 | C2 | semidirect |
| 4. #28381912 | C2 | semidirect |
| 5. #28381911 | C2 | semidirect |
| 6. #28381906 | C2 | semidirect |
| 7. C2×#20296771 | C2 | semidirect |
| 8. C2×#41×C443 | C2 | semidirect |
| 12. #20296787 | C22 | semidirect |
| 13. C2×Dic886 | C22 | semidirect |
| 14. C2×D1772 | C22 | semidirect |
| 17. #20296777 | C22 | semidirect |
| 18. #20296775 | C22 | semidirect |
| 19. #20296774 | C22 | semidirect |
| 20. #20296772 | C22 | semidirect |
| 21. #20296771 | C22 | semidirect |
| 22. #20296771 | C22 | semidirect |
| 23. C2×C443⋊C8 | C22 | semidirect |
| 27. #41×C443 | C22 | semidirect |
| 28. C2×Q8×C443 | C22 | semidirect |
| 30. C2×D4×C443 | C22 | semidirect |
| 81. C443 | #575 | semidirect |
| 84. C2×#41 | D443 | semidirect |
| 98. #41 | C2×D443 | semidirect |
| 100. C2×Q8 | C2×D443 | semidirect |
| 104. C2×D4 | C2×D443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20296787 | 2 |
| #28381917 | 2 |
| #28381916 | 2 |
| #28381912 | 2 |
| #28381911 | 2 |
| #28381906 | 2 |
| C2×#20296771 | 2 |
| C2×#41×C443 | 2 |
| #575 | 443 |