Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 2. #27161279 | C2 | semidirect |
| 3. #27160832 | C2 | semidirect |
| 4. #27160822 | C2 | semidirect |
| 5. C8×Q8×C197 | C2 | semidirect |
| 40. Q8×C197 | D8 | semidirect |
| 48. C8×C197 | SD16 | semidirect |
| 64. C197 | #1668 | semidirect |
| 68. C8×Q8 | D197 | semidirect |
| 99. Q8 | D1576 | semidirect |
| 113. C8 | #15691345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161456 | 2 |
| #27161279 | 2 |
| #27160832 | 2 |
| #27160822 | 2 |
| C8×Q8×C197 | 2 |
| #1668 | 197 |