Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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×#20263269 | C2 | semidirect |
| 3. #27161317 | C2 | semidirect |
| 4. #27160883 | C2 | semidirect |
| 5. #27160881 | C2 | semidirect |
| 6. #27160858 | C2 | semidirect |
| 7. C2×Q32×C197 | C2 | semidirect |
| 85. C197 | #2189 | semidirect |
| 88. C2×Q32 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263349 | 2 |
| C2×#20263269 | 2 |
| #27161317 | 2 |
| #27160883 | 2 |
| #27160881 | 2 |
| #27160858 | 2 |
| C2×Q32×C197 | 2 |
| #2189 | 197 |