Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
412 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 133 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. #27161634 | C2 | semidirect |
| 3. #27161477 | C2 | semidirect |
| 4. #27161429 | C2 | semidirect |
| 5. #27161425 | C2 | semidirect |
| 6. #27161305 | C2 | semidirect |
| 7. SD16×Dic197 | C2 | semidirect |
| 8. C4×C8×D197 | C2 | semidirect |
| 9. #492×C197 | C2 | semidirect |
| 79. C4×D197 | SD16 | semidirect |
| 90. C8×C197 | #41 | semidirect |
| 112. C197 | #3167 | semidirect |
| 117. #492 | D197 | semidirect |
| 203. C8 | #15691357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| #27161627 | 2 |
| #27161477 | 2 |
| #27161429 | 2 |
| #27161425 | 2 |
| #27161305 | 2 |
| SD16×Dic197 | 2 |
| C4×C8×D197 | 2 |
| #492×C197 | 2 |
| #3167 | 197 |