Finite Group DatabasebetaFinite Group DatabasebetaOrder 25408.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #27163121 | C2 | semidirect |
| 2. C2×#20263716 | C2 | semidirect |
| 3. #27163103 | C2 | semidirect |
| 4. #27163031 | C2 | semidirect |
| 5. #27163013 | C2 | semidirect |
| 6. #27163012 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C397 | C2 | semidirect |
| 53. C397 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27163121 | 2 |
| C2×#20263716 | 2 |
| #27163103 | 2 |
| #27163031 | 2 |
| #27163013 | 2 |
| #27163012 | 2 |
| AGL(1,ℤ/8)×C397 | 2 |
| #472 | 397 |