Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
996 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#15691346 | C2 | semidirect |
| 2. C2×#20263305 | C2 | semidirect |
| 3. #27161230 | C2 | direct (N × H) |
| 4. C2×#20263247 | C2 | semidirect |
| 5. C2×C22⋊#13096802 | C2 | semidirect |
| 7. C22×Dic394 | C22 | semidirect |
| 9. C2×#15691346 | C22 | semidirect |
| 10. C22×#13096802 | C22 | semidirect |
| 12. #20263305 | C22 | semidirect |
| 13. C2×C4⋊Dic197 | C22 | semidirect |
| 16. #20263247 | C22 | semidirect |
| 17. C22⋊#13096802 | C22 | semidirect |
| 27. C2×Dic394 | C23 | semidirect |
| 32. C2×#13096802 | C23 | semidirect |
| 34. C4⋊Dic197 | C23 | semidirect |
| 73. C23×C197 | SD16 | semidirect |
| 97. C22×C197 | C2×SD16 | semidirect |
| 107. C2×C197 | #450 | semidirect |
| 111. C197 | C2×#450 | semidirect |
| 178. C23 | #15691346 | semidirect |
| 209. C22 | C2×#15691346 | semidirect |
| 219. C2 | #27161230 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691346 | 2 |
| C2×#20263305 | 2 |
| #27161230 | 2 |
| C2×#20263247 | 2 |
| C2×C22⋊#13096802 | 2 |
| C23×D4×C197 | 2 |
| C2×#450 | 197 |