Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
176 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #27160831 | C2 | semidirect |
| 4. Q8⋊#13096802 | C2 | semidirect |
| 6. #27160801 | C2 | semidirect |
| 7. C8×Q8×C197 | C2 | semidirect |
| 25. #15691345 | C8 | semidirect |
| 50. #13096802 | C2×C8 | semidirect |
| 52. Q8×C197 | C2×C8 | semidirect |
| 77. C197 | SD16⋊C8 | semidirect |
| 79. C8×Q8 | D197 | semidirect |
| 121. Q8 | C8×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15691345 | 2 |
| C8×D788 | 2 |
| #27160831 | 2 |
| Q8⋊#13096802 | 2 |
| #27160806 | 2 |
| #27160801 | 2 |
| C8×Q8×C197 | 2 |
| SD16⋊C8 | 197 |