Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #28380742 | C2 | semidirect |
| 2. #28380741 | C2 | semidirect |
| 3. #28380738 | C2 | semidirect |
| 4. #28380738 | C2 | semidirect |
| 5. #28380736 | C2 | semidirect |
| 6. #28380736 | C2 | semidirect |
| 7. #28380734 | C2 | semidirect |
| 8. #28380733 | C2 | semidirect |
| 12. #28380722 | C2 | semidirect |
| 13. #28380721 | C2 | semidirect |
| 14. #28380719 | C2 | semidirect |
| 15. C22⋊Q8×C439 | C2 | semidirect |
| 97. C439 | #563 | semidirect |
| 113. C22⋊Q8 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28380742 | 2 |
| #28380741 | 2 |
| #28380738 | 2 |
| #28380736 | 2 |
| #28380734 | 2 |
| #28380733 | 2 |
| #28380729 | 2 |
| #28380726 | 2 |
| #28380725 | 2 |
| #28380722 | 2 |
| #28380721 | 2 |
| #28380719 | 2 |
| C22⋊Q8×C439 | 2 |
| #563 | 439 |