Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. D4×Dic439 | C2 | semidirect |
| 3. #28380705 | C2 | semidirect |
| 4. #28380674 | C2 | semidirect |
| 5. #28380665 | C2 | semidirect |
| 6. #28380653 | C2 | semidirect |
| 7. #102×C439 | C2 | semidirect |
| 11. #20296314 | C4 | semidirect |
| 22. D1756 | C2×C4 | semidirect |
| 28. C439⋊C8 | C2×C4 | semidirect |
| 31. D4×C439 | C2×C4 | semidirect |
| 53. C439 | #442 | semidirect |
| 60. #102 | D439 | semidirect |
| 79. D4 | C4×D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20296314 | 2 |
| D4×Dic439 | 2 |
| #28380705 | 2 |
| #28380674 | 2 |
| #28380665 | 2 |
| #28380653 | 2 |
| #102×C439 | 2 |
| #442 | 439 |