Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #27163974 | C2 | semidirect |
| 5. C2×C4×C199⋊C8 | C2 | semidirect |
| 6. #27163782 | C2 | semidirect |
| 7. #339×C199 | C2 | semidirect |
| 10. #20263963 | C4 | semidirect |
| 16. #20263883 | C4 | semidirect |
| 17. #20263878 | C4 | semidirect |
| 18. #20263875 | C4 | semidirect |
| 98. C199 | #1764 | semidirect |
| 106. #339 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263963 | 2 |
| C2×#20263883 | 2 |
| #27164012 | 2 |
| #27163974 | 2 |
| C2×C4×C199⋊C8 | 2 |
| #27163782 | 2 |
| #339×C199 | 2 |
| #1764 | 199 |