Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #27161117 | C2 | semidirect |
| 3. #27160881 | C2 | semidirect |
| 4. C2×M32×C197 | C2 | semidirect |
| 8. C2×D1576 | C4 | semidirect |
| 11. #20263260 | C22 | semidirect |
| 15. C2×C16×C197 | C22 | semidirect |
| 62. C197 | #2140 | semidirect |
| 65. C2×M32 | D197 | semidirect |
| 76. C2×C16 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1576 | 2 |
| #27161117 | 2 |
| #27160881 | 2 |
| C2×M32×C197 | 2 |
| #2140 | 197 |