Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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. #27161452 | C2 | semidirect |
| 3. #27161370 | C2 | semidirect |
| 4. #27161369 | C2 | semidirect |
| 5. #27160822 | C2 | semidirect |
| 6. #27160808 | C2 | semidirect |
| 7. D4⋊C8×C197 | C2 | semidirect |
| 11. #20263326 | C22 | semidirect |
| 19. C4⋊#13096802 | C22 | semidirect |
| 23. C4⋊C8×C197 | C22 | semidirect |
| 24. C4×C8×C197 | C22 | semidirect |
| 65. D788 | SD16 | semidirect |
| 74. D4×C197 | SD16 | semidirect |
| 108. C197 | #1629 | semidirect |
| 116. D4⋊C8 | D197 | semidirect |
| 130. C4⋊C8 | C2×D197 | semidirect |
| 133. C4×C8 | C2×D197 | semidirect |
| 178. D4 | #15691347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D788 | 2 |
| #27161452 | 2 |
| #27161370 | 2 |
| #27161369 | 2 |
| #27160822 | 2 |
| #27160808 | 2 |
| D4⋊C8×C197 | 2 |
| #1629 | 197 |