Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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. #27163982 | C2 | semidirect |
| 3. #27163754 | C2 | semidirect |
| 4. #27163751 | C2 | semidirect |
| 5. C2×#95×C199 | C2 | semidirect |
| 6. C2×#15691886 | C4 | semidirect |
| 9. #20263934 | C4 | semidirect |
| 11. #20263929 | C4 | semidirect |
| 16. #20263914 | C4 | semidirect |
| 24. C2×Dic398 | C2×C4 | semidirect |
| 25. C2×D796 | C2×C4 | semidirect |
| 32. C4⋊Dic199 | C2×C4 | semidirect |
| 33. C4⋊Dic199 | C2×C4 | semidirect |
| 119. C199 | #1504 | semidirect |
| 123. C2×#95 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164529 | 2 |
| #27163982 | 2 |
| #27163754 | 2 |
| #27163751 | 2 |
| C2×#95×C199 | 2 |
| #1504 | 199 |