Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 1. D4×D788 | C2 | semidirect |
| 2. #27161455 | C2 | semidirect |
| 3. #27161271 | C2 | semidirect |
| 4. #27160822 | C2 | semidirect |
| 5. D4⋊#13096802 | C2 | semidirect |
| 6. #27160806 | C2 | semidirect |
| 7. #459×C197 | C2 | semidirect |
| 17. C4⋊#13096802 | C22 | semidirect |
| 19. C4×#13096802 | C22 | semidirect |
| 21. #127×C197 | C22 | semidirect |
| 23. C4⋊C8×C197 | C22 | semidirect |
| 66. D788 | D8 | semidirect |
| 81. D4×C197 | D8 | semidirect |
| 117. C197 | #1619 | semidirect |
| 122. #459 | D197 | semidirect |
| 132. #127 | C2×D197 | semidirect |
| 139. C4⋊C8 | C2×D197 | semidirect |
| 194. D4 | #15691343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D788 | 2 |
| #27161455 | 2 |
| #27161271 | 2 |
| #27160822 | 2 |
| D4⋊#13096802 | 2 |
| #27160806 | 2 |
| #459×C197 | 2 |
| #1619 | 197 |