Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161446 | C2 | semidirect |
| 4. #27161431 | C2 | semidirect |
| 5. #27161430 | C2 | semidirect |
| 6. #27161429 | C2 | semidirect |
| 9. #487×C197 | C2 | semidirect |
| 106. C197 | #3139 | semidirect |
| 114. #487 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| C4⋊Q8×D197 | 2 |
| #27161446 | 2 |
| #27161431 | 2 |
| #27161430 | 2 |
| #27161429 | 2 |
| #27161086 | 2 |
| C4×#15691341 | 2 |
| #487×C197 | 2 |
| #3139 | 197 |