Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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. #27161019 | C2 | semidirect |
| 4. #27161016 | C2 | semidirect |
| 5. #27161011 | C2 | semidirect |
| 6. #27161006 | C2 | semidirect |
| 7. #27161004 | C2 | semidirect |
| 9. C4×C4⋊Dic197 | C2 | semidirect |
| 10. C4×#15691335 | C2 | semidirect |
| 11. C4×C22⋊C4×C197 | C2 | semidirect |
| 137. C197 | #2395 | semidirect |
| 149. C4×C22⋊C4 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D197 | 2 |
| C2×#20263285 | 2 |
| #27161019 | 2 |
| #27161016 | 2 |
| #27161011 | 2 |
| #27161006 | 2 |
| #27161004 | 2 |
| #27160995 | 2 |
| C4×C4⋊Dic197 | 2 |
| C4×#15691335 | 2 |
| C4×C22⋊C4×C197 | 2 |
| #2395 | 197 |