Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D788 | C2 | semidirect |
| 3. #27161430 | C2 | semidirect |
| 4. #27161411 | C2 | semidirect |
| 5. #27161364 | C2 | semidirect |
| 6. #27161307 | C2 | semidirect |
| 7. #27161284 | C2 | semidirect |
| 8. #27161216 | C2 | semidirect |
| 9. C8×D788 | C2 | semidirect |
| 10. #103×D197 | C2 | semidirect |
| 11. C4×SD16×C197 | C2 | semidirect |
| 82. D788 | SD16 | semidirect |
| 94. Q8×C197 | #41 | semidirect |
| 128. C197 | #3298 | semidirect |
| 138. C4×SD16 | D197 | semidirect |
| 213. Q8 | #15691358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D788 | 2 |
| #27161734 | 2 |
| #27161430 | 2 |
| #27161411 | 2 |
| #27161364 | 2 |
| #27161307 | 2 |
| #27161284 | 2 |
| #27161216 | 2 |
| C8×D788 | 2 |
| #103×D197 | 2 |
| C4×SD16×C197 | 2 |
| #3298 | 197 |