Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27161482 | C2 | semidirect |
| 3. #27161356 | C2 | semidirect |
| 4. #27160826 | C2 | semidirect |
| 5. D4⋊#13096802 | C2 | semidirect |
| 6. #27160806 | C2 | semidirect |
| 7. #461×C197 | C2 | semidirect |
| 97. C197 | #1647 | semidirect |
| 102. #461 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161733 | 2 |
| #27161482 | 2 |
| #27161356 | 2 |
| #27160826 | 2 |
| D4⋊#13096802 | 2 |
| #27160806 | 2 |
| #461×C197 | 2 |
| #1647 | 197 |