Finite Group DatabasebetaFinite Group DatabasebetaOrder 28352.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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. #41×D443 | C2 | semidirect |
| 2. #28381918 | C2 | semidirect |
| 3. #28381915 | C2 | semidirect |
| 4. #28381913 | C2 | semidirect |
| 5. #28381910 | C2 | semidirect |
| 6. #28381908 | C2 | semidirect |
| 7. #28381906 | C2 | semidirect |
| 8. C2×#20296770 | C2 | semidirect |
| 9. #135×C443 | C2 | semidirect |
| 12. #20296787 | C22 | semidirect |
| 15. Q8×D443 | C22 | semidirect |
| 17. D4×D443 | C22 | semidirect |
| 20. Dic1772 | C22 | semidirect |
| 21. #20296777 | C22 | semidirect |
| 22. #20296776 | C22 | semidirect |
| 23. #20296775 | C22 | semidirect |
| 24. #20296774 | C22 | semidirect |
| 25. D3544 | C22 | semidirect |
| 26. #20296772 | C22 | semidirect |
| 27. #20296770 | C22 | semidirect |
| 28. #20296770 | C22 | semidirect |
| 29. C2×C443⋊C8 | C22 | semidirect |
| 30. #41×C443 | C22 | semidirect |
| 31. Q16×C443 | C22 | semidirect |
| 32. SD16×C443 | C22 | semidirect |
| 33. D8×C443 | C22 | semidirect |
| 34. C2×C8×C443 | C22 | semidirect |
| 75. C443 | #575 | semidirect |
| 84. #135 | D443 | semidirect |
| 91. #41 | C2×D443 | semidirect |
| 99. Q16 | C2×D443 | semidirect |
| 103. SD16 | C2×D443 | semidirect |
| 106. D8 | C2×D443 | semidirect |
| 110. C2×C8 | C2×D443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D443 | 2 |
| #28381918 | 2 |
| #28381915 | 2 |
| #28381913 | 2 |
| #28381910 | 2 |
| #28381908 | 2 |
| #28381906 | 2 |
| C2×#20296770 | 2 |
| #135×C443 | 2 |
| #575 | 443 |