Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 2. C2×Q8×D439 | C2 | semidirect |
| 3. #28380742 | C2 | semidirect |
| 4. #28380729 | C2 | semidirect |
| 5. #28380728 | C2 | semidirect |
| 6. #28380725 | C2 | semidirect |
| 7. #28380723 | C2 | semidirect |
| 8. #28380722 | C2 | semidirect |
| 9. #28380719 | C2 | semidirect |
| 10. #28380701 | C2 | semidirect |
| 11. C22⋊Q8×C439 | C2 | semidirect |
| 83. C439 | #536 | semidirect |
| 94. C22⋊Q8 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20296329 | 2 |
| C2×Q8×D439 | 2 |
| #28380742 | 2 |
| #28380729 | 2 |
| #28380728 | 2 |
| #28380725 | 2 |
| #28380723 | 2 |
| #28380722 | 2 |
| #28380719 | 2 |
| #28380701 | 2 |
| C22⋊Q8×C439 | 2 |
| #536 | 439 |