Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. #27161456 | C2 | semidirect |
| 2. #27161455 | C2 | semidirect |
| 3. #27161455 | C2 | semidirect |
| 4. #27161453 | C2 | semidirect |
| 5. #27161427 | C2 | semidirect |
| 6. #27160801 | C2 | semidirect |
| 7. #486×C197 | C2 | semidirect |
| 50. #13096802 | D8 | semidirect |
| 81. C197 | #1721 | semidirect |
| 88. #486 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161456 | 2 |
| #27161455 | 2 |
| #27161453 | 2 |
| #27161427 | 2 |
| #27160801 | 2 |
| #486×C197 | 2 |
| #1721 | 197 |