Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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. #27161845 | C2 | semidirect |
| 3. #27161097 | C2 | semidirect |
| 4. #27161073 | C2 | semidirect |
| 5. #27161047 | C2 | semidirect |
| 6. #27160843 | C2 | semidirect |
| 7. #344×C197 | C2 | semidirect |
| 11. #20263359 | C4 | semidirect |
| 13. #20263354 | C4 | semidirect |
| 118. C197 | #1881 | semidirect |
| 125. #344 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161879 | 2 |
| #27161845 | 2 |
| #27161097 | 2 |
| #27161073 | 2 |
| #27161047 | 2 |
| #27160843 | 2 |
| #344×C197 | 2 |
| #1881 | 197 |