Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#20269398 | C2 | semidirect |
| 2. C2×D3352 | C2 | semidirect |
| 3. C2×#20269396 | C2 | semidirect |
| 4. #27211714 | C2 | semidirect |
| 5. #27211707 | C2 | semidirect |
| 6. #27211628 | C2 | semidirect |
| 7. C2×SD16×C419 | C2 | semidirect |
| 29. C419⋊C8 | D4 | semidirect |
| 37. C8×C419 | D4 | semidirect |
| 54. C419 | #496 | semidirect |
| 57. C2×SD16 | D419 | semidirect |
| 92. C8 | C22⋊D419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269398 | 2 |
| C2×D3352 | 2 |
| C2×#20269396 | 2 |
| #27211714 | 2 |
| #27211707 | 2 |
| #27211628 | 2 |
| C2×SD16×C419 | 2 |
| #496 | 419 |