Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #27161487 | C2 | semidirect |
| 4. #27161482 | C2 | semidirect |
| 5. #27161477 | C2 | semidirect |
| 6. #27161475 | C2 | semidirect |
| 9. #500×C197 | C2 | semidirect |
| 43. #15691341 | Q8 | semidirect |
| 79. #13096802 | C2×Q8 | semidirect |
| 87. C8×C197 | C2×Q8 | semidirect |
| 106. C197 | #3165 | semidirect |
| 112. #500 | D197 | semidirect |
| 194. C8 | Q8×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| C4⋊Q8×D197 | 2 |
| #27161487 | 2 |
| #27161482 | 2 |
| #27161477 | 2 |
| #27161475 | 2 |
| #27161120 | 2 |
| C4×#15691341 | 2 |
| #500×C197 | 2 |
| #3165 | 197 |