Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 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. C2×#20263262 | C2 | semidirect |
| 5. #27161034 | C2 | semidirect |
| 6. #27160839 | C2 | semidirect |
| 7. #336×C197 | C2 | semidirect |
| 14. #20263251 | C4 | semidirect |
| 15. #20263251 | C4 | semidirect |
| 16. #20263248 | C4 | semidirect |
| 17. #20263248 | C4 | semidirect |
| 105. C197 | #1929 | semidirect |
| 113. #336 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263262 | 2 |
| C2×#20263254 | 2 |
| #27161076 | 2 |
| #27161045 | 2 |
| #27161034 | 2 |
| #27160839 | 2 |
| #336×C197 | 2 |
| #1929 | 197 |