Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #27161106 | C2 | semidirect |
| 5. C2×C4×#13096802 | C2 | semidirect |
| 6. #27160843 | C2 | semidirect |
| 7. #339×C197 | C2 | semidirect |
| 14. #20263249 | C4 | semidirect |
| 15. #20263246 | C4 | semidirect |
| 90. C197 | #1937 | semidirect |
| 98. #339 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161106 | 2 |
| C2×#20263254 | 2 |
| #27161073 | 2 |
| #27161047 | 2 |
| C2×C4×#13096802 | 2 |
| #27160843 | 2 |
| #339×C197 | 2 |
| #1937 | 197 |