Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D197 | C2 | semidirect |
| 3. #27161374 | C2 | semidirect |
| 4. #27161370 | C2 | semidirect |
| 5. #27161366 | C2 | semidirect |
| 6. #27161362 | C2 | semidirect |
| 7. #27161358 | C2 | semidirect |
| 8. #27161120 | C2 | semidirect |
| 9. #27161101 | C2 | semidirect |
| 11. #477×C197 | C2 | semidirect |
| 44. #15691359 | Q8 | semidirect |
| 88. D788 | C2×Q8 | semidirect |
| 105. Q8×C197 | C2×Q8 | semidirect |
| 137. C197 | #3079 | semidirect |
| 142. #477 | D197 | semidirect |
| 226. Q8 | Q8×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D197 | 2 |
| C4×#15691359 | 2 |
| #27161374 | 2 |
| #27161370 | 2 |
| #27161366 | 2 |
| #27161362 | 2 |
| #27161358 | 2 |
| #27161120 | 2 |
| #27161101 | 2 |
| #27161079 | 2 |
| #477×C197 | 2 |
| #3079 | 197 |