Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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. #27161034 | C2 | semidirect |
| 5. #27160851 | C2 | semidirect |
| 6. #27160849 | C2 | semidirect |
| 7. #405×C197 | C2 | semidirect |
| 15. C2×#15691341 | C4 | semidirect |
| 16. C2×C8×D197 | C4 | semidirect |
| 18. #20263244 | C4 | semidirect |
| 19. #20263242 | C4 | semidirect |
| 106. C197 | #1757 | semidirect |
| 112. #405 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263332 | 2 |
| #27161061 | 2 |
| #27161052 | 2 |
| #27161034 | 2 |
| #27160851 | 2 |
| #27160849 | 2 |
| #405×C197 | 2 |
| #1757 | 197 |