Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 3. #27161421 | C2 | semidirect |
| 4. #27161415 | C2 | semidirect |
| 5. #27161410 | C2 | semidirect |
| 6. #27161121 | C2 | semidirect |
| 7. #27161089 | C2 | semidirect |
| 25. #20263260 | C22 | semidirect |
| 26. #20263258 | C22 | semidirect |
| 27. #20263251 | C22 | semidirect |
| 28. #20263251 | C22 | semidirect |
| 116. C197 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263305 | 2 |
| C2×#20263285 | 2 |
| #27161421 | 2 |
| #27161415 | 2 |
| #27161410 | 2 |
| #27161121 | 2 |
| #27161089 | 2 |
| #407×C197 | 2 |
| #3095 | 197 |