Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #28380738 | C2 | semidirect |
| 2. #28380734 | C2 | semidirect |
| 3. #28380732 | C2 | semidirect |
| 4. #28380728 | C2 | semidirect |
| 5. #28380719 | C2 | semidirect |
| 7. C4×D1756 | C2 | semidirect |
| 8. C4×D1756 | C2 | semidirect |
| 9. #28380700 | C2 | semidirect |
| 10. C42×D439 | C2 | semidirect |
| 11. C4×Q8×C439 | C2 | semidirect |
| 74. C439 | #529 | semidirect |
| 82. C4×Q8 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28380738 | 2 |
| #28380734 | 2 |
| #28380732 | 2 |
| #28380728 | 2 |
| #28380719 | 2 |
| #28380718 | 2 |
| C4×D1756 | 2 |
| #28380700 | 2 |
| C42×D439 | 2 |
| C4×Q8×C439 | 2 |
| #529 | 439 |