Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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×#20263356 | C2 | semidirect |
| 2. C22×#15691348 | C2 | semidirect |
| 3. #27161650 | C2 | semidirect |
| 4. #27161241 | C2 | semidirect |
| 5. #27161235 | C2 | semidirect |
| 6. #27161088 | C2 | semidirect |
| 7. #27161075 | C2 | semidirect |
| 8. #27161046 | C2 | semidirect |
| 140. C197 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263356 | 2 |
| C22×#15691348 | 2 |
| #27161650 | 2 |
| #27161241 | 2 |
| #27161235 | 2 |
| #27161088 | 2 |
| #27161075 | 2 |
| #27161046 | 2 |
| C2×2−1+4×C197 | 2 |
| #3011 | 197 |