Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161431 | C2 | semidirect |
| 3. #27161420 | C2 | semidirect |
| 4. #27161356 | C2 | semidirect |
| 5. #27161318 | C2 | semidirect |
| 6. #27161289 | C2 | semidirect |
| 7. #27161239 | C2 | semidirect |
| 8. C4×#15691345 | C2 | semidirect |
| 9. D4×#13096802 | C2 | semidirect |
| 10. #27161073 | C2 | semidirect |
| 11. #556×C197 | C2 | semidirect |
| 125. C197 | #3302 | semidirect |
| 127. #556 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161734 | 2 |
| #27161431 | 2 |
| #27161420 | 2 |
| #27161356 | 2 |
| #27161318 | 2 |
| #27161289 | 2 |
| #27161239 | 2 |
| C4×#15691345 | 2 |
| D4×#13096802 | 2 |
| #27161073 | 2 |
| #556×C197 | 2 |
| #3302 | 197 |