Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
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. #27161650 | C2 | semidirect |
| 2. C2×#20263313 | C2 | semidirect |
| 3. C2×#20263253 | C2 | semidirect |
| 4. #27161084 | C2 | semidirect |
| 5. C2×#20263244 | C2 | semidirect |
| 6. #27160840 | C2 | semidirect |
| 130. C197 | #2003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161650 | 2 |
| C2×#20263313 | 2 |
| C2×#20263253 | 2 |
| #27161084 | 2 |
| C2×#20263244 | 2 |
| #27160840 | 2 |
| C2×AGL(1,ℤ/8)×C197 | 2 |
| #2003 | 197 |