Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. #27164036 | C2 | semidirect |
| 3. #27164035 | C2 | semidirect |
| 4. #27164015 | C2 | semidirect |
| 5. #27163991 | C2 | semidirect |
| 6. #27163984 | C2 | semidirect |
| 7. #416×C199 | C2 | semidirect |
| 10. #20264002 | C4 | semidirect |
| 12. #20264001 | C4 | semidirect |
| 20. C2×#15691870 | C22 | semidirect |
| 21. #20263914 | C22 | semidirect |
| 29. C22×C8×C199 | C22 | semidirect |
| 30. #117×C199 | C22 | semidirect |
| 166. C199 | #1794 | semidirect |
| 172. #416 | D199 | semidirect |
| 189. C22×C8 | C2×D199 | semidirect |
| 191. #117 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164854 | 2 |
| #27164036 | 2 |
| #27164035 | 2 |
| #27164015 | 2 |
| #27163991 | 2 |
| #27163984 | 2 |
| #416×C199 | 2 |
| #1794 | 199 |