Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27161279 | C2 | semidirect |
| 3. #27161210 | C2 | semidirect |
| 4. #27160829 | C2 | semidirect |
| 5. #27160823 | C2 | semidirect |
| 6. #27160822 | C2 | semidirect |
| 7. #460×C197 | C2 | semidirect |
| 52. #13096802 | SD16 | semidirect |
| 86. C197 | #1688 | semidirect |
| 90. #460 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161455 | 2 |
| #27161279 | 2 |
| #27161210 | 2 |
| #27160829 | 2 |
| #27160823 | 2 |
| #27160822 | 2 |
| #460×C197 | 2 |
| #1688 | 197 |