Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 3. #27160904 | C2 | semidirect |
| 4. #27160884 | C2 | semidirect |
| 5. #27160882 | C2 | semidirect |
| 7. #366×C197 | C2 | semidirect |
| 66. C197 | #2236 | semidirect |
| 71. #366 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161321 | 2 |
| #107×D197 | 2 |
| #27160904 | 2 |
| #27160884 | 2 |
| #27160882 | 2 |
| #27160858 | 2 |
| #366×C197 | 2 |
| #2236 | 197 |