Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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. #27211716 | C2 | semidirect |
| 2. #27211708 | C2 | semidirect |
| 3. #27211708 | C2 | semidirect |
| 4. #27211696 | C2 | semidirect |
| 5. #27211696 | C2 | semidirect |
| 6. #27211695 | C2 | semidirect |
| 7. #27211695 | C2 | semidirect |
| 8. #27211694 | C2 | semidirect |
| 9. #27211683 | C2 | semidirect |
| 13. C2×Dic419⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D419 | C2 | semidirect |
| 15. C22⋊Q8×C419 | C2 | semidirect |
| 54. C22⋊D419 | Q8 | semidirect |
| 101. C419 | #554 | semidirect |
| 111. C22⋊Q8 | D419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27211716 | 2 |
| #27211708 | 2 |
| #27211696 | 2 |
| #27211695 | 2 |
| #27211694 | 2 |
| #27211683 | 2 |
| C4×C22⋊D419 | 2 |
| (C22⋊D419)⋊C4 | 2 |
| C2×Dic419⋊C4 | 2 |
| C4⋊C4×D419 | 2 |
| C22⋊Q8×C419 | 2 |
| #554 | 419 |