Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#20263262 | C2 | semidirect |
| 3. C2×#20263261 | C2 | semidirect |
| 6. #27160843 | C2 | semidirect |
| 7. #341×C197 | C2 | semidirect |
| 99. C2×D197 | #108 | semidirect |
| 113. C197 | #1855 | semidirect |
| 121. #341 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D197 | 2 |
| C2×#20263262 | 2 |
| C2×#20263261 | 2 |
| #27161042 | 2 |
| C2×#20263238 | 2 |
| #27160843 | 2 |
| #341×C197 | 2 |
| #1855 | 197 |