Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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×#20296316 | C2 | semidirect |
| 3. #28380750 | C2 | semidirect |
| 4. #28380678 | C2 | semidirect |
| 5. #28380662 | C2 | semidirect |
| 6. #28380659 | C2 | semidirect |
| 7. #137×C439 | C2 | semidirect |
| 51. C439 | #471 | semidirect |
| 53. #137 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28380768 | 2 |
| C2×#20296316 | 2 |
| #28380750 | 2 |
| #28380678 | 2 |
| #28380662 | 2 |
| #28380659 | 2 |
| #137×C439 | 2 |
| #471 | 439 |