Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 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. #27161364 | C2 | semidirect |
| 4. #27160830 | C2 | semidirect |
| 5. #27160826 | C2 | semidirect |
| 7. C8×Q8×C197 | C2 | semidirect |
| 54. Q8×C197 | SD16 | semidirect |
| 62. C8×C197 | SD16 | semidirect |
| 79. C197 | #1666 | semidirect |
| 84. C8×Q8 | D197 | semidirect |
| 126. Q8 | #15691347 | semidirect |
| 142. C8 | #15691345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161452 | 2 |
| #27161364 | 2 |
| #27161279 | 2 |
| #27160830 | 2 |
| #27160826 | 2 |
| #27160822 | 2 |
| C8×Q8×C197 | 2 |
| #1666 | 197 |