Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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×#20263980 | C2 | semidirect |
| 2. C22×#15691871 | C2 | semidirect |
| 3. C2×#20263872 | C2 | semidirect |
| 4. C2×#20263871 | C2 | semidirect |
| 5. #27163985 | C2 | semidirect |
| 6. #27163782 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C199 | C2 | semidirect |
| 132. C199 | #2018 | semidirect |
| 135. C2×AGL(1,ℤ/8) | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263980 | 2 |
| C22×#15691871 | 2 |
| C2×#20263872 | 2 |
| C2×#20263871 | 2 |
| #27163985 | 2 |
| #27163782 | 2 |
| C2×AGL(1,ℤ/8)×C199 | 2 |
| #2018 | 199 |