Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161802 | C2 | semidirect |
| 2. #27161789 | C2 | semidirect |
| 3. #27161434 | C2 | semidirect |
| 4. #27161430 | C2 | semidirect |
| 5. #27161387 | C2 | semidirect |
| 6. #27161370 | C2 | semidirect |
| 8. #27161285 | C2 | semidirect |
| 9. C4×#15691347 | C2 | semidirect |
| 11. C8×Q8×C197 | C2 | semidirect |
| 120. C197 | #3360 | semidirect |
| 130. C8×Q8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161802 | 2 |
| #27161789 | 2 |
| #27161434 | 2 |
| #27161430 | 2 |
| #27161387 | 2 |
| #27161370 | 2 |
| #27161295 | 2 |
| #27161285 | 2 |
| C4×#15691347 | 2 |
| C4×D1576 | 2 |
| C8×Q8×C197 | 2 |
| #3360 | 197 |