Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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. #27161103 | C2 | semidirect |
| 3. C2×#20263254 | C2 | semidirect |
| 4. C43×C197 | C2 | semidirect |
| 7. #20263326 | C4 | semidirect |
| 8. #20263323 | C4 | semidirect |
| 9. #20263314 | C4 | semidirect |
| 36. C42×C197 | D4 | semidirect |
| 63. C4×C197 | #104 | semidirect |
| 72. C197 | #1962 | semidirect |
| 77. C43 | D197 | semidirect |
| 109. C42 | D788 | semidirect |
| 137. C4 | #20263254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161629 | 2 |
| #27161103 | 2 |
| C2×#20263254 | 2 |
| C43×C197 | 2 |
| #1962 | 197 |