Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#20296318 | C2 | semidirect |
| 3. C2×#20296317 | C2 | semidirect |
| 4. #28380723 | C2 | semidirect |
| 5. #28380663 | C2 | semidirect |
| 6. (C2×D439)⋊C8 | C2 | semidirect |
| 7. #102×C439 | C2 | semidirect |
| 9. C2×Dic878 | C22 | semidirect |
| 17. C2×C439⋊C8 | C22 | semidirect |
| 21. C2×C8×C439 | C22 | semidirect |
| 22. C4⋊C4×C439 | C22 | semidirect |
| 54. C2×D439 | SD16 | semidirect |
| 66. C439 | #450 | semidirect |
| 73. #102 | D439 | semidirect |
| 86. C2×C8 | C2×D439 | semidirect |
| 88. C4⋊C4 | C2×D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D439 | 2 |
| C2×#20296318 | 2 |
| C2×#20296317 | 2 |
| #28380723 | 2 |
| #28380663 | 2 |
| (C2×D439)⋊C8 | 2 |
| #102×C439 | 2 |
| #450 | 439 |