Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C4⋊Dic197 | C2 | semidirect |
| 3. #27161415 | C2 | semidirect |
| 4. #27161410 | C2 | semidirect |
| 5. #27161398 | C2 | semidirect |
| 6. #27161393 | C2 | semidirect |
| 7. #27161121 | C2 | semidirect |
| 8. #27161081 | C2 | semidirect |
| 9. #407×C197 | C2 | semidirect |
| 27. #20263260 | C22 | semidirect |
| 28. #20263258 | C22 | semidirect |
| 29. #20263251 | C22 | semidirect |
| 30. #20263248 | C22 | semidirect |
| 130. C197 | #3092 | semidirect |
| 140. #407 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161590 | 2 |
| C22×C4⋊Dic197 | 2 |
| #27161415 | 2 |
| #27161410 | 2 |
| #27161398 | 2 |
| #27161393 | 2 |
| #27161121 | 2 |
| #27161081 | 2 |
| #407×C197 | 2 |
| #3092 | 197 |