Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #28380737 | C2 | semidirect |
| 2. #28380735 | C2 | semidirect |
| 3. #28380731 | C2 | semidirect |
| 4. #28380726 | C2 | semidirect |
| 5. #28380722 | C2 | semidirect |
| 7. C4×Dic878 | C2 | semidirect |
| 8. C4×D1756 | C2 | semidirect |
| 9. C4×C22⋊D439 | C2 | semidirect |
| 10. #28380700 | C2 | semidirect |
| 11. C2×C42×C439 | C2 | semidirect |
| 74. C439 | #529 | semidirect |
| 86. C2×C42 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28380737 | 2 |
| #28380735 | 2 |
| #28380731 | 2 |
| #28380726 | 2 |
| #28380722 | 2 |
| #28380717 | 2 |
| C4×Dic878 | 2 |
| C4×D1756 | 2 |
| C4×C22⋊D439 | 2 |
| #28380700 | 2 |
| C2×C42×C439 | 2 |
| #529 | 439 |