Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27161365 | C2 | semidirect |
| 4. C8×Dic394 | C2 | semidirect |
| 5. #27160824 | C2 | semidirect |
| 7. #334×C197 | C2 | semidirect |
| 46. Dic394 | SD16 | semidirect |
| 62. C8×C197 | SD16 | semidirect |
| 79. C197 | #1666 | semidirect |
| 85. #334 | D197 | semidirect |
| 142. C8 | #15691347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161452 | 2 |
| #27161365 | 2 |
| #27161280 | 2 |
| C8×Dic394 | 2 |
| #27160824 | 2 |
| #27160822 | 2 |
| #334×C197 | 2 |
| #1666 | 197 |