Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 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. #27161425 | C2 | semidirect |
| 3. #27161360 | C2 | semidirect |
| 4. #27161285 | C2 | semidirect |
| 5. #27160806 | C2 | semidirect |
| 6. #27160806 | C2 | semidirect |
| 7. #331×C197 | C2 | semidirect |
| 11. #20263326 | C22 | semidirect |
| 21. C4×#13096802 | C22 | semidirect |
| 23. C4⋊C8×C197 | C22 | semidirect |
| 24. C4⋊C8×C197 | C22 | semidirect |
| 62. D788 | SD16 | semidirect |
| 109. C197 | #1639 | semidirect |
| 115. #331 | D197 | semidirect |
| 129. C4⋊C8 | C2×D197 | semidirect |
| 130. C4⋊C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161714 | 2 |
| #27161425 | 2 |
| #27161360 | 2 |
| #27161285 | 2 |
| #27160806 | 2 |
| #331×C197 | 2 |
| #1639 | 197 |