Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
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×#20296329 | C2 | semidirect |
| 2. #28380774 | C2 | semidirect |
| 3. #28380773 | C2 | semidirect |
| 4. #28380769 | C2 | semidirect |
| 5. #28380768 | C2 | semidirect |
| 6. #28380763 | C2 | semidirect |
| 7. C2×#20296313 | C2 | semidirect |
| 8. C2×#41×C439 | C2 | semidirect |
| 12. #20296329 | C22 | semidirect |
| 13. C2×Dic878 | C22 | semidirect |
| 14. C2×D1756 | C22 | semidirect |
| 17. #20296319 | C22 | semidirect |
| 18. #20296317 | C22 | semidirect |
| 19. #20296316 | C22 | semidirect |
| 20. #20296314 | C22 | semidirect |
| 21. #20296313 | C22 | semidirect |
| 22. #20296313 | C22 | semidirect |
| 23. C2×C439⋊C8 | C22 | semidirect |
| 27. #41×C439 | C22 | semidirect |
| 28. C2×Q8×C439 | C22 | semidirect |
| 30. C2×D4×C439 | C22 | semidirect |
| 81. C439 | #575 | semidirect |
| 84. C2×#41 | D439 | semidirect |
| 98. #41 | C2×D439 | semidirect |
| 100. C2×Q8 | C2×D439 | semidirect |
| 104. C2×D4 | C2×D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20296329 | 2 |
| #28380774 | 2 |
| #28380773 | 2 |
| #28380769 | 2 |
| #28380768 | 2 |
| #28380763 | 2 |
| C2×#20296313 | 2 |
| C2×#41×C439 | 2 |
| #575 | 439 |