Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#20263351 | C2 | semidirect |
| 2. C2×#20263323 | C2 | semidirect |
| 3. #27161469 | C2 | semidirect |
| 4. #27161455 | C2 | semidirect |
| 5. #27161453 | C2 | semidirect |
| 6. C4×#15691342 | C2 | semidirect |
| 7. #532×C197 | C2 | semidirect |
| 11. C2×#15691345 | C22 | semidirect |
| 12. C2×#15691343 | C22 | semidirect |
| 17. #20263237 | C22 | semidirect |
| 18. C4×#13096802 | C22 | semidirect |
| 20. C4⋊Q8×C197 | C22 | semidirect |
| 21. #127×C197 | C22 | semidirect |
| 22. #124×C197 | C22 | semidirect |
| 35. #15691342 | D4 | semidirect |
| 57. #13096802 | C2×D4 | semidirect |
| 83. C4×C197 | AGL(1,ℤ/8) | semidirect |
| 90. C197 | #3151 | semidirect |
| 93. #532 | D197 | semidirect |
| 106. C4⋊Q8 | C2×D197 | semidirect |
| 110. #127 | C2×D197 | semidirect |
| 111. #124 | C2×D197 | semidirect |
| 174. C4 | #20263351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| C2×#20263323 | 2 |
| #27161469 | 2 |
| #27161455 | 2 |
| #27161453 | 2 |
| C4×#15691342 | 2 |
| #532×C197 | 2 |
| #3151 | 197 |