Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#20263285 | C2 | semidirect |
| 3. #27161421 | C2 | semidirect |
| 4. #27161415 | C2 | semidirect |
| 5. #27161410 | C2 | semidirect |
| 6. #27161404 | C2 | semidirect |
| 7. #27161398 | C2 | semidirect |
| 8. #27161393 | C2 | semidirect |
| 9. #27161117 | C2 | semidirect |
| 10. #27161076 | C2 | semidirect |
| 11. C2×C22⋊C8×C197 | C2 | semidirect |
| 30. #20263260 | C22 | semidirect |
| 31. #20263260 | C22 | semidirect |
| 32. #20263258 | C22 | semidirect |
| 33. #20263258 | C22 | semidirect |
| 34. #20263251 | C22 | semidirect |
| 35. #20263251 | C22 | semidirect |
| 36. #20263248 | C22 | semidirect |
| 37. #20263248 | C22 | semidirect |
| 143. C197 | #3091 | semidirect |
| 155. C2×C22⋊C8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161590 | 2 |
| C2×#20263285 | 2 |
| #27161421 | 2 |
| #27161415 | 2 |
| #27161410 | 2 |
| #27161404 | 2 |
| #27161398 | 2 |
| #27161393 | 2 |
| #27161117 | 2 |
| #27161076 | 2 |
| C2×C22⋊C8×C197 | 2 |
| #3091 | 197 |