Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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×#20263254 | C2 | semidirect |
| 3. C2×#20263253 | C2 | semidirect |
| 4. C2×#20263252 | C2 | semidirect |
| 5. M16×Dic197 | C2 | semidirect |
| 6. C4×#15691337 | C2 | semidirect |
| 7. C2×#104×C197 | C2 | semidirect |
| 10. #20263324 | C4 | semidirect |
| 11. #20263322 | C4 | semidirect |
| 12. #20263315 | C4 | semidirect |
| 13. #20263313 | C4 | semidirect |
| 45. #15691342 | D4 | semidirect |
| 71. M16×C197 | D4 | semidirect |
| 140. Dic197 | #104 | semidirect |
| 148. C197 | #1980 | semidirect |
| 154. C2×#104 | D197 | semidirect |
| 206. M16 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161625 | 2 |
| C2×#20263254 | 2 |
| C2×#20263253 | 2 |
| C2×#20263252 | 2 |
| M16×Dic197 | 2 |
| C4×#15691337 | 2 |
| C2×#104×C197 | 2 |
| #1980 | 197 |