Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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. #27211717 | C2 | semidirect |
| 2. #27211708 | C2 | semidirect |
| 3. #27211698 | C2 | semidirect |
| 4. #27211695 | C2 | semidirect |
| 5. #27211694 | C2 | semidirect |
| 6. Q8×Dic419 | C2 | semidirect |
| 9. C2×C4⋊Dic419 | C2 | semidirect |
| 10. C4⋊C4×D419 | C2 | semidirect |
| 11. C22⋊Q8×C419 | C2 | semidirect |
| 37. C22⋊D419 | Q8 | semidirect |
| 74. C419 | #554 | semidirect |
| 81. C22⋊Q8 | D419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27211717 | 2 |
| #27211708 | 2 |
| #27211698 | 2 |
| #27211695 | 2 |
| #27211694 | 2 |
| Q8×Dic419 | 2 |
| C4×C22⋊D419 | 2 |
| (C22⋊D419)⋊C4 | 2 |
| C2×C4⋊Dic419 | 2 |
| C4⋊C4×D419 | 2 |
| C22⋊Q8×C419 | 2 |
| #554 | 419 |