Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161734 | C2 | semidirect |
| 3. #27161477 | C2 | semidirect |
| 4. #27161402 | C2 | semidirect |
| 5. #27161396 | C2 | semidirect |
| 6. #27161369 | C2 | semidirect |
| 7. #27161359 | C2 | semidirect |
| 8. #27161329 | C2 | semidirect |
| 9. #27161158 | C2 | semidirect |
| 10. #27161120 | C2 | semidirect |
| 11. C4×D8×C197 | C2 | semidirect |
| 101. C8×C197 | #41 | semidirect |
| 127. C197 | #3354 | semidirect |
| 137. C4×D8 | D197 | semidirect |
| 229. C8 | #15691358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161794 | 2 |
| #27161734 | 2 |
| #27161477 | 2 |
| #27161402 | 2 |
| #27161396 | 2 |
| #27161369 | 2 |
| #27161359 | 2 |
| #27161329 | 2 |
| #27161158 | 2 |
| #27161120 | 2 |
| C4×D8×C197 | 2 |
| #3354 | 197 |