Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. #27164139 | C2 | semidirect |
| 3. #27164130 | C2 | semidirect |
| 4. #27163842 | C2 | semidirect |
| 5. #27163829 | C2 | semidirect |
| 6. #27163795 | C2 | semidirect |
| 7. #361×C199 | C2 | semidirect |
| 11. #20263899 | C4 | semidirect |
| 12. #20263896 | C4 | semidirect |
| 23. Dic796 | C2×C4 | semidirect |
| 25. D1592 | C2×C4 | semidirect |
| 32. C199⋊C16 | C2×C4 | semidirect |
| 68. C199 | AGL(1,ℤ/16) | semidirect |
| 74. #361 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164454 | 2 |
| #27164139 | 2 |
| #27164130 | 2 |
| #27163842 | 2 |
| #27163829 | 2 |
| #27163795 | 2 |
| #361×C199 | 2 |
| AGL(1,ℤ/16) | 199 |