Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161794 | C2 | semidirect |
| 2. #27161733 | C2 | semidirect |
| 3. #27161477 | C2 | semidirect |
| 4. #27161404 | C2 | semidirect |
| 5. #27161398 | C2 | semidirect |
| 6. #27161370 | C2 | semidirect |
| 7. #27161360 | C2 | semidirect |
| 8. #27161332 | C2 | semidirect |
| 9. C4×D1576 | C2 | semidirect |
| 10. #27161121 | C2 | semidirect |
| 11. #436×C197 | C2 | semidirect |
| 101. C8×C197 | #41 | semidirect |
| 127. C197 | #3354 | semidirect |
| 138. #436 | D197 | semidirect |
| 229. C8 | #15691357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161794 | 2 |
| #27161733 | 2 |
| #27161477 | 2 |
| #27161404 | 2 |
| #27161398 | 2 |
| #27161370 | 2 |
| #27161360 | 2 |
| #27161332 | 2 |
| C4×D1576 | 2 |
| #27161121 | 2 |
| #436×C197 | 2 |
| #3354 | 197 |