Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
180 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 51. C8×C197 | Q16 | semidirect |
| 63. C197 | #1707 | semidirect |
| 115. C8 | #15691348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161482 | 2 |
| #27161477 | 2 |
| #27161458 | 2 |
| #27161431 | 2 |
| #27161429 | 2 |
| C8×#13096802 | 2 |
| #498×C197 | 2 |
| #1707 | 197 |