Finite Group DatabasebetaFinite Group DatabasebetaOrder 28352.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#20296788 | C2 | semidirect |
| 2. C2×D4×D443 | C2 | semidirect |
| 3. #28381913 | C2 | direct (N × H) |
| 4. C2×#20296774 | C2 | semidirect |
| 5. C2×D3544 | C2 | semidirect |
| 6. C2×#20296772 | C2 | semidirect |
| 7. C2×#20296770 | C2 | semidirect |
| 8. C2×SD16×C443 | C2 | semidirect |
| 11. #20296788 | C22 | semidirect |
| 14. C2×D1772 | C22 | semidirect |
| 17. D4×D443 | C22 | semidirect |
| 20. #20296774 | C22 | semidirect |
| 21. D3544 | C22 | semidirect |
| 22. #20296772 | C22 | semidirect |
| 23. #20296770 | C22 | semidirect |
| 24. C2×C443⋊C8 | C22 | semidirect |
| 25. C2×Q8×C443 | C22 | semidirect |
| 27. SD16×C443 | C22 | semidirect |
| 28. C2×C8×C443 | C22 | semidirect |
| 38. D1772 | C23 | semidirect |
| 44. C443⋊C8 | C23 | semidirect |
| 47. Q8×C443 | C23 | semidirect |
| 52. C8×C443 | C23 | semidirect |
| 68. C2×C443 | AGL(1,ℤ/8) | semidirect |
| 73. C443 | C2×AGL(1,ℤ/8) | semidirect |
| 79. C2×SD16 | D443 | semidirect |
| 86. C2×Q8 | C2×D443 | semidirect |
| 97. SD16 | C2×D443 | semidirect |
| 102. C2×C8 | C2×D443 | semidirect |
| 110. Q8 | C22×D443 | semidirect |
| 126. C8 | C22×D443 | semidirect |
| 145. C2 | #28381913 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20296788 | 2 |
| C2×D4×D443 | 2 |
| #28381913 | 2 |
| C2×#20296774 | 2 |
| C2×D3544 | 2 |
| C2×#20296772 | 2 |
| C2×#20296770 | 2 |
| C2×SD16×C443 | 2 |
| C2×AGL(1,ℤ/8) | 443 |