Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27161429 | C2 | semidirect |
| 3. #27161407 | C2 | semidirect |
| 4. #27161364 | C2 | semidirect |
| 5. #27161310 | C2 | semidirect |
| 6. #27161281 | C2 | semidirect |
| 7. #27161218 | C2 | semidirect |
| 8. C4×#15691345 | C2 | semidirect |
| 9. D4×#13096802 | C2 | semidirect |
| 10. C2×#20263250 | C2 | semidirect |
| 11. D4×Q8×C197 | C2 | semidirect |
| 94. Q8×C197 | #41 | semidirect |
| 95. D4×C197 | SD16 | semidirect |
| 128. C197 | #3298 | semidirect |
| 130. D4×Q8 | D197 | semidirect |
| 213. Q8 | #15691357 | semidirect |
| 217. D4 | #15691345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161733 | 2 |
| #27161429 | 2 |
| #27161407 | 2 |
| #27161364 | 2 |
| #27161310 | 2 |
| #27161281 | 2 |
| #27161218 | 2 |
| C4×#15691345 | 2 |
| D4×#13096802 | 2 |
| C2×#20263250 | 2 |
| D4×Q8×C197 | 2 |
| #3298 | 197 |