Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
210 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27160825 | C2 | semidirect |
| 5. Q8⋊#13096802 | C2 | semidirect |
| 6. Q8⋊#13096802 | C2 | semidirect |
| 7. #557×C197 | C2 | semidirect |
| 63. Q8×C197 | SD16 | semidirect |
| 90. C197 | #1626 | semidirect |
| 92. #557 | D197 | semidirect |
| 146. Q8 | #15691345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161427 | 2 |
| #27161279 | 2 |
| #27160825 | 2 |
| Q8⋊#13096802 | 2 |
| #557×C197 | 2 |
| #1626 | 197 |