Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
104 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C419 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C23×C419 |
| prime radical | AGL(1,ℤ/8)×C419 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C419 ◁ C2×C4×C419 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #137×C419 | C2 | semidirect |
| 3. C2×SD16×C419 | C2 | semidirect |
| 4. #131×C419 | C2 | semidirect |
| 5. #108×C419 | C2 | semidirect |
| 6. #101×C419 | C2 | semidirect |
| 7. #100×C419 | C2 | semidirect |
| 51. C419 | #471 | direct (N × H) |
| 52. #471 | C419 | direct (N × H) |
| 53. #137 | C2×C419 | semidirect |
| 55. C2×SD16 | C2×C419 | semidirect |
| 56. #131 | C2×C419 | semidirect |
| 57. #108 | C2×C419 | semidirect |
| 58. #101 | C2×C419 | semidirect |
| 59. #100 | C2×C419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #137×C419 | 2 |
| AGL(1,ℤ/8)×C419 | 2 |
| C2×SD16×C419 | 2 |
| #131×C419 | 2 |
| #108×C419 | 2 |
| #101×C419 | 2 |
| #100×C419 | 2 |
| #471 | 419 |