Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #28380791 | C2 | semidirect |
| 2. #28380790 | C2 | semidirect |
| 3. #28380776 | C2 | semidirect |
| 4. #28380775 | C2 | semidirect |
| 5. #28380772 | C2 | semidirect |
| 6. #28380764 | C2 | semidirect |
| 7. #28380763 | C2 | semidirect |
| 8. C2×#20296319 | C2 | semidirect |
| 9. Q16×D439 | C2 | semidirect |
| 10. #28380751 | C2 | semidirect |
| 11. #137×C439 | C2 | semidirect |
| 87. C439 | #578 | semidirect |
| 94. #137 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28380791 | 2 |
| #28380790 | 2 |
| #28380776 | 2 |
| #28380775 | 2 |
| #28380772 | 2 |
| #28380764 | 2 |
| #28380763 | 2 |
| C2×#20296319 | 2 |
| Q16×D439 | 2 |
| #28380751 | 2 |
| #137×C439 | 2 |
| #578 | 439 |